Complete reset of SGS2 (factory reset not sufficient)
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.