I don't actually remember where it gets created; I think a popup will say where. I have a dmp file in the BtS install folder (where the EXE is located), so I guess that's the place. (Or maybe I moved it there; I seem to recall that they get created in the Windows temp folder?) When I open it in Visual Studio (screenshot attached), I learn that there was a segmentation fault at code address such and such in the EXE, and I see a (unreliable) stack trace, showing other functions in the EXE, all in disassembled native code. That's not nothing, but it's far from sufficient for fixing a bug or working around it. If the crash had occurred in the DLL (which is more commonly the case when a DLL mod crashes) and the DLL had been compiled with debug symbols, then one could, I think, in theory, debug it based on the dmp – however, Visual Studio is very finicky about the debug symbols, I think it needs access to the exact same version of the source code that the crashed DLL was compiled from. Much easier to debug it based on a savegame, i.e. to reproduce the crash with the debugger attached. The only potential use of the crash dumps generated by the EXE that I can see is to debug a crash that can't be reproduced locally, i.e. when the player who gets the crash doesn't know how to debug and the developer who does know doesn't get the crash. Not sure if any modders have used crash dumps productively.
I guess you've already tested whether Dave_uk's (original) mod crashes when (auto-)playing one of the LoR scenarios and whether LoR combined with GEM crashes. So the problems seem to arise from the combination of Dave_uk's changes and GEM? You could try the previous version of Dave_uk's mod; that one had supposedly been tested more. Beyond that, I think you'd either have to get into
DLL modding in order to use the Visual Studio debugger (or at least to enable runtime assertions) or experiment with changes to the GEM files. Not sure if that's just a WBSave; could try removing all but 2 players etc. For a crash after ending the turn, the last few lines in PythonDbg.log and the BBAI log might provide some clue. The logs will just show things that happened some time before (or possibly just before) the crash, e.g. "The AI is choosing what to produce in York." Not necessarily helpful.