Hi Ben,
Yes, the logs will be in C:\Trimble Synchronizer Data\<CONTROLLER NAME>\Trimble Siteworks Diagnostic Data.
We were just made aware of a potential bug in the heights while doing exactly that move base workflow, and I also agree that saving the intermediate base positions would be beneficial.
So if you get those logs and can open a support case with your dealer, that is the proper way to handle crashes, so that we have a support ticket and the issue tracked properly. Also, when doing the case, you can save a lot of back and forth by being sure to include a detailed description of the steps that cause the crash, and including the project folder, so that we can try to replicate it.