Well, I've given this more thought (recent weather helping), and I've pretty much made up my mind: 2 sets of tires, keep the PS2s for summer and buy winter tires and wheels for winter. The Michelin PA3 or PA4 is at the top of my list. Now trying to decide on wheels.
BMW NW wants $2800 for a set of 270M with PA3. Most likely mounted with TPMS. That seems like a lot, but if my maths are correct, $1K tires, $275 TPMS, $125ish mounting... That makes the wheelset $1400. Can I something decent aftermarket for a lot less?