I realised this is a very specific question, but I am wondering if there is a way to install FreeBSD on a machine using only SSH access to a Ubuntu LiveCD on the server?
Yes, You Can! (But it's entirely unsupported and may cause your hair to fall out, arms to grow out of the top of your head, and other hideous mutations!)
The particular disgusting hackery you're looking for is called The Depenguinator, but be warned: It's 4 years old, and potentially suffering from serious bit rot. If you discover and fix said bit rot I'm sure the author would be happy to accept patches.
If you're not married to an Ubuntu LiveCD a better option would be to use a FreeBSD LiveCD (Like Freesbie) -- I know you can run
The straightest way is:
Install minimal FreeBSD without swap on a [virtual] host near you and
Install allowed OS on a minimal possible partition on a target host. Bootmanager is a MUST.
Create FreeBSD slice/partitions on a free disk space.
Then boot allowed OS and
In VNC select FreeBSD from bootmanager's list.
From FreeBSD delete partition where allowed OS lives and make swap here.
The only trouble you can get in - is a different numbering of slices on a dumped/restored hosts.