[Agrajag]

I find it more likely that the problem is in specific calculations in battle resolutions rather than a problem with random numbers. For example, using a different function for checking morale in the replay phase then the hosting phase.
What you are talking about (Ewierl) is IIRC a bug that has been squashed long ago where on different OSs the random code got evaluated differently (specifically, in a "if(random()>random)()" on some OSs the left one was resolved first and on other the right one), which lead to wildly different results. This case is a bit more subtle, and I'm guessing that it's an SP game, so was hosted and replayed on exactly the same machine.
I'm pretty sure a save that shows the bug would be useful for Illwinter, especially if you can get a save from one turn before it happens.