Complete reset of SGS2 (factory reset not sufficient) background here:
Recovering internal memory on SGS2 (CWM, not root, boot to recovery only)

The problem is that having recovered that data, and having done a factory reset (wiping /data, /cache), the phone still doesn't boot. It goes to the Galaxy S2 screen, and then turns off (not getting to SAMSUNG screen). 

So I assume there must be a problem with /system.

Is there a log somewhere on the phone that I could access that might show me what the problem is? Otherwise should I try to flash other roms (or reflash the stock rom?) in the hope that this would resolve it?

Many thanks!
I think you should just flash another ROM. You will still have all your data on the Internal SD so no need to worry about that. This would wipe your /system. So what you want to do is follow the standard procedure of installing a new Custom ROM and you should be good to go without any data loss (Eg. Pictures, Videos etc. You still lose any app data not backed up on the cloud).
A great site with recommendations which I use for my own phone is GalaxyS2Root.
Some ROM recommendations I can give you from my own personal usage are AOKP JB MR2, Resurrection Remix v5. Try to avoid the ones with battery drain issues and you should be fine.
Going thru the phone log with your phone not booting up is a hassle which is unnecessary in this case. Just do the above and you'll be fine.