I have absolutely no artillery (recall my earlier cunning decision not to build any), so the only way I can defeat the garrison on the victory hex is to surround it and pulverize it with infantry fire. This I manage to do, but it takes a whole day. In the process, two of my brigades become disordered.
(Questions for the experts: what's the best way to get them undisordered? If I see 0% by the column and line formation options, that means it's fruitless to click those buttons, right? So does one just skip a turn repeatedly? Also, is spacebar the same as skipping a turn?)
Also, I have only one supply caisson. Now that I've read the manual, I think this is partly a consequence of (1) being cut off on the main map and (2) not ordering a rise in the Strategic Supply level of this army group on the main map.
Anyway, after I take that one victory hex, a sole CSA brigade mounts a furious counterattack from the east. It sweeps aside two of my brigades and heads right into the center of town -- and then makes a beeline for my disordered units, routing them instantly. It caps all this off by destroying my sole supply caisson, or at least I think that's what happened. The supply unit seems to be lying on its side, broken. Here's a look at the marauding CSA unit, this time in "chit view" (NATO symbols):
