Bleh. Well, that was completely unsatisfying. For whatever reason, the AI proved utterly unable to cope with being flanked. I took my initial tiger on a move-fast blitz down a side street in the village, and started poking my nose out in each of the cross streets, destroying a few tanks each time. Of course, that was made easier by the AI's stubborn refusal to acknowledge I was behind its tanks. After knocking out three, I noticed the remainder were facing away from me, towards the Axis start location...and never tried turning until they were engaged, by which time, of course, it was too late.
So I took out virtually all the Allied tanks with my starting Tiger due to an AI glitch. Meh.