Okay, here are the files. I don't have the "SynchLog" option (perhaps because we're using different versions?), but otherwise I followed your instructions to the letter.
I think I might know what the problem is. After I'd won the conquest victory (following your instructions), it said it couldn't access a certain game file. The file PythonErr reads:
Traceback (most recent call last):
File "CvScreensInterface", line 131, in showReplay
RuntimeError: unidentifiable C++ exception
ERR: Python function showReplay failed, module CvScreensInterface
Now one of the many times I've reinstalled the game, I remember it saying that a certain file - and I'm quite sure it was CvScreensInterface - on my DVD was corrupted, but I just wiped the disc clean, and told it to try again, and it worked. It could be I need to get hold of that file off the Net somehow.