Tournament XPanded - Version 1.6.3.hf2 (and hf1) fixes the save issue with BL1.2.0. There may be another issue around item modifiers that has yet to be figured out - hf2 adds extra error handling around that to try and prevent it from being an issue. (Or you can turn off item modifiers in the experimental settings of the mod).
I've been playing all morning with it on the latest BL1.2.1 that came out today and I've had no problems saving or crashing. If you do have problems you can send me the logfile on nexus or I can tell you how to turn on more diagnostics if you're in a mind to help troubleshoot it.