Provision with the latest Ubuntu template from the control panel. At the time of writing this was...

Provision with the latest Ubuntu template from the control panel. At the time of writing this was ubuntu18img.
Once the machine is booted, login as root over the noVNC console (you may wish to SSH in to easy copy&paste but have a noVNC console open as you'll need it at points) and run:
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apt update && apt -y dist-upgrade && apt -y autoremove

Stop the cloud init scripts running and setup grub so you can see the boot menu easily:

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mv /etc/cloud /etc/cloud.bak
rm /etc/default/grub.d/50-cloudimg-settings.cfg 
sed -e 's/GRUB_TIMEOUT_STYLE=hidden/GRUB_TIMEOUT_STYLE=menu/g'    -e 's/GRUB_TIMEOUT=0/GRUB_TIMEOUT=10/g'    -i.bak /etc/default/grub
update-grub

We then create a simple script to ease tasks when we drop to the initramfs shell

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cat <<EOF>/script.sh
cp /run/mnt/sbin/resize2fs /run/mnt/sbin/e2fsck /run/mnt/script.sh /
umount /run/mnt
/e2fsck -f /dev/sda1
/resize2fs /dev/sda1 3G
sync; reboot
EOF

Time for the first reboot - keep an eye on the noVNC as you'll need it to get into the initramfs
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reboot
Go to 'Advanced options for Ubuntu' and press 'e' when the latest kernel's recovery mode option is selected.
Edit the 'linux' line and remove all options but add 'ro init=/bin/sh'
Press Ctrl-X to boot
You'll now be at an initramfs prompt
Once here you'll need to make a directory, mount the root drive, copy the script we made earlier and run it. After running it the machine will reboot.
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mkdir /run/mnt mount /dev/sda1 /run/mnt cp /run/mnt/script.sh / sh /script.sh
Reboot to your previous ubuntu install. On logging in you'll now see you have a small root (/) partition of only a few gig rather than the previous one that took the whole disk.
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root@system:~# df -hP / Filesystem Size Used Avail Use% Mounted on /dev/sda1 2.9G 1.5G 1.4G 52% /

We'll now shrink the partition table to match this size, and create a new partition to hold a copy of the current install. Because we are working on an active disk we'll need to reboot after this

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start=$(sfdisk -d /dev/sda | grep '^/dev/sda1 :' | awk '{print $4}' | cut -f 1 -d \,)
uuid=$(sfdisk -d /dev/sda | grep '^/dev/sda1 :' | awk '{print $8}' | cut -f 1 -d \,)
(sfdisk -d /dev/sda | grep -v '^/dev/sda'; echo "/dev/sda1 : start=$start, size=3G, type=0FC63DAF-8483-4772-8E79-3D69D8477DE4, $uuid"; sfdisk -d /dev/sda | grep '^/dev/sda1[45]') | sfdisk --force /dev/sda

size=$(sfdisk -d /dev/sda | grep '^/dev/sda1 ' | awk '{print $6}' | cut -f 1 -d \,)
last=$(sfdisk -d /dev/sda | grep ^last-lba | awk '{print $2}')
delta=0
(sfdisk -d /dev/sda | grep -v '^/dev/sda' ; sfdisk -d /dev/sda | grep '^/dev/sda1 :'; echo "/dev/sda13 : start=$(($(($last-$size))-$delta)), size=$(($size+$delta)), type=0FC63DAF-8483-4772-8E79-3D69D8477DE4"; sfdisk -d /dev/sda | grep '^/dev/sda1[45] :') | sfdisk --force /dev/sda
reboot

Now we have sda1 - the shrunk root from the initial install, sda13 - a bare parition to copy the initial install to along with sda14 and sda15 for Boot and EFI. Lets copy sda1 to sda13:

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root@system:~# dd if=/dev/sda1 of=/dev/sda13 bs=4M 
768+0 records in
768+0 records out
3221225472 bytes (3.2 GB, 3.0 GiB) copied, 7.27464 s, 443 MB/s
root@system:~# e2fsck -y /dev/sda13
e2fsck 1.44.1 (24-Mar-2018)
cloudimg-rootfs: recovering journal
Setting free inodes count to 288387 (was 288395)
Setting free blocks count to 360142 (was 360214)
cloudimg-rootfs: clean, 98685/387072 files, 426290/786432 blocks
root@system:~# tune2fs -O metadata_csum_seed /dev/sda13
tune2fs 1.44.1 (24-Mar-2018)
root@system:~# tune2fs -U random /dev/sda13
tune2fs 1.44.1 (24-Mar-2018)
root@system:~# e2fsck -fy /dev/sda13
e2fsck 1.44.1 (24-Mar-2018)
Pass 1: Checking inodes, blocks, and sizes
Pass 2: Checking directory structure
Pass 3: Checking directory connectivity
Pass 4: Checking reference counts
Pass 5: Checking group summary information
cloudimg-rootfs: 98685/387072 files (0.3% non-contiguous), 426290/786432 blocks
root@system:~# tune2fs -O ^metadata_csum_seed /dev/sda13
tune2fs 1.44.1 (24-Mar-2018)
Recalculating checksums could take some time.
Proceed anyway (or wait 5 seconds to proceed) ? (y,N) <proceeding>
root@system:~# tune2fs -L cloudimg-orig /dev/sda13
tune2fs 1.44.1 (24-Mar-2018)
root@system:~# e2fsck -y /dev/sda13
e2fsck 1.44.1 (24-Mar-2018)
cloudimg-orig: clean, 98685/387072 files, 426290/786432 blocks

We'll then mount sda13 and make some changes to make it bootable

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mount /dev/sda13 /mnt/
for i in sys proc dev boot/efi; do mount --bind /$i /mnt/$i; done
rm /mnt/etc/resolv.conf
cp /etc/resolv.conf /mnt/etc/resolv.conf
chroot /mnt
sed -i.bak -e 's/LABEL=cloudimg-rootfs/LABEL=cloudimg-orig/g' /etc/fstab 
apt -y install grub-pc
update-initramfs -k all -u
update-grub
grub-install /dev/sda
exit

for i in sys proc dev boot/efi; do umount /mnt/$i; done
umount /mnt

Now for another reboot, this time you should find yourself on sda13 as the root - you can confirm with df. It's an exact copy so you shouldn't see anything different other than this.
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root@system:~# df -hP / Filesystem Size Used Avail Use% Mounted on /dev/sda13 2.9G 1.5G 1.4G 53% /

So now we can re-use sda1 so lets delete it first

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sfdisk --delete /dev/sda 1
update-initramfs -k all -u
update-grub
grub-install /dev/sda

Optional Step: Having the partitions in a strange order (sda14 and 15) seems odd to me so I re-number them also. Another reboot here to make sure we have a clean working system
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sfdisk -d /dev/sda | sed -e 's/sda14/sda1/g' -e 's/sda15/sda2/g' | sfdisk --force /dev/sda reboot
Now lets create the new partition for LUKS and LVM. Again, because it's an active disk we'll need to reboot :-(
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echo ",,," | sfdisk -a --force /dev/sda reboot

Now we setup LUKS and LVM - you might want a different layout here:

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cryptsetup luksFormat /dev/sda3 
cryptsetup luksOpen /dev/sda3 cryptroot
pvcreate /dev/mapper/cryptroot 
vgcreate system_vg /dev/mapper/cryptroot 
lvcreate -L4G -n ROOT system_vg
lvcreate -L2G -n VAR system_vg
lvcreate -L4G -n DOCKER system_vg
lvcreate -L1G -n HOME system_vg
lvcreate -L4G -n SWAP system_vg 
mkswap /dev/system_vg/SWAP
for i in ROOT VAR DOCKER HOME; do mkfs.ext4 /dev/system_vg/$i; done

Now is the time to reinstall to the new structure. First step mount it all:

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mount /dev/system_vg/ROOT /mnt/
mkdir /mnt/var /mnt/home
mount /dev/system_vg/VAR /mnt/var
mount /dev/system_vg/HOME /mnt/home
mkdir -p /mnt/var/lib/docker
mount /dev/system_vg/DOCKER /mnt/var/lib/docker

Next step install debootstrap and install a base system to it. I'm using groovy here:

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1 2	apt install debootstrap debootstrap --arch amd64 groovy /mnt/ https://mirrors.chroot.ro/ubuntu

We can now chroot into that install and create an apt sources file, generate an fstab and install some required packages:

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mkdir /mnt/boot/efi
for i in sys proc dev boot/efi; do mount --bind /$i /mnt/$i; done
chroot /mnt/

cat<<EOF>/etc/apt/sources.list
deb http://archive.ubuntu.com/ubuntu groovy main multiverse universe
deb http://security.ubuntu.com/ubuntu groovy-security main multiverse universe
EOF

( mount | grep ^/ | while read line; do  uuid=$(blkid -o value --match-tag UUID $(echo $line | cut -f 1));  echo UUID=$uuid $(echo $line | cut -f 3 -d ' ') $(echo $line | cut -f 5 -d ' ') defaults 0 0; done ; echo "tmpfs /tmp tmpfs size=4G 0 0") > /etc/fstab

apt -y install linux-virtual lvm2 grub-pc cryptsetup openssh-server
sed -e 's/GRUB_TIMEOUT_STYLE=hidden/GRUB_TIMEOUT_STYLE=menu/g'    -e 's/GRUB_TIMEOUT=0/GRUB_TIMEOUT=10/g'    -i.bak /etc/default/grub

Because I'm using LUKS I also setup CRYPTODISK settings for grub and create the keyfile script

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echo 'GRUB_ENABLE_CRYPTODISK=y' >> /etc/default/grub

dd bs=512 count=4 if=/dev/urandom of=/crypto_keyfile.bin
cryptsetup luksAddKey /dev/sda3 /crypto_keyfile.bin
chmod 000 /crypto_keyfile.bin
echo "cryptroot UUID=$(blkid /dev/sda3 -o value | head -n 1) /crypto_keyfile.bin luks,keyscript=/bin/cat" >> /etc/crypttab 

cat <<EOF>/etc/initramfs-tools/hooks/crypto_keyfile
#!/bin/sh
cp /crypto_keyfile.bin "\${DESTDIR}"
EOF
chmod +x /etc/initramfs-tools/hooks/crypto_keyfile

Now time to regenerate the initramfs, update grub and install it

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update-initramfs -k all -u
update-grub
grub-install /dev/sda

At this point I also update the root passwd and generate some users and configure the network

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passwd root
adduser --ingroup users jamesr
adduser jamesr adm 
adduser jamesr sudo
cat <<EOF>/etc/netplan/01-netcfg.yaml
network:
  version: 2
  renderer: networkd
  ethernets:
    ens18:
      dhcp4: false
      dhcp6: false
      addresses: [ "w.x.y.z/22" ]
      gateway4: "w.x.y.z"
      nameservers:
        addresses:
          - "1.1.1.1"
          - "1.0.0.1"
EOF

You can now drop out of the chroot, unmount everything, delete the old install, grow the paritions to fullsize and do a final reboot into your new system

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exit # To leave the chroot
for i in sys proc dev boot/efi; do umount /mnt/$i; done
for i in var/lib/docker/ home var; do umount /mnt/$i; done
umount /mnt
apt install cloud-guest-utils fdisk
sfdisk --delete /dev/sda 13
growpart /dev/sda 3
reboot

You'll just want to max on the PV Size like so as the final step... no reboot needed this time! :D
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pvresize /dev/mapper/cryptroot