Recovering internal memory on SGS2 (CWM, not root, boot to recovery only)
I initially installed CWM v5 (as zip from CWM site), but that appears mount the internal sd card memory with root permissions only. I finally tried CWM 6.0.4.5 (again as zip, not from cwm site). The zip failed verification, so I couldn't install it. However, in v5, there's an option to ignore that, so I was able to run v6. It seems to run fine so far, and the storage is mounted correctly, and I can now pull with adb! 

So - solution:
- Boot into stock recovery
- Install CWM v5 (from cwm site) from sd card (as zip)
- Use that to install CWM v6 from sd card (as zip)
- Then use adb to pull /storage/sdcard0. (adb will not preserve time stamps, but you can do a "ls -laRe" if you want particular file stamps

So in this way I was able to retrieve the contents of the internal sd card. Full details
http://www.sciencemedianetwork.org/Blog/20140304_Samsung_Galaxy_S2_data_recovery

However, after factory reset, the phone still doesn't boot. Follow up question here:
Complete reset of SGS2 (factory reset not sufficient)