Failed to verify installESG.dmg on install mountain lion
For anyone coming across this in the future, there's 2 issues with this route:


The new file system introduced in Sierra means that the startup SSD must be APFS and can not be extended journaled. This means that with a brand new hard drive without a startup volume one can not restore directly using time machine onto the SSD. You need to install (High) Sierra first and then restore from time machine afterwards
Mountain Lion OS was apparently not a free OS and in Apple's own words this is why the internet restore is failing at the end


The 3 ways to resolve this are either:


Restore from a pre Sierra Time Machine image, then from this image upgrade to high sierra and then finally restore from the time machine image
Restore from the Mountain Lion recovery CD, then upgrade to High Sierra and restore from time machine
Obtain bootable High Sierra ISO from USB, install High Sierra and then restore from Time Machine


I hope this helps someone. This is my first time having to do disaster recovery in MacOS and I've been really surprised how un-user friendly this experience is when coming coming from an old machine