Thanks - that what I suspected as well, although I thought I was doing a full wipe (including /system) in TWRP, but maybe not?
Anyway, I somehow got it working last night after formatting /data and then flashing the last CM stable release (CM-10.1.3, p3110). Got the tablet to boot and setup and everything. Maybe there was something conflicting in the data folder, or that there was no more space on the internal SD. Guess I won't know now..
But I decided to flash the latest Omnirom instead, to get a 4.4 rom. Seems to be working fine now. Thanks for the reply!