In reply to paulpitcher:
> b) Do my mountaineering in ski boots...
Yes.
For steep alpine snow/ice routes, ski mountaineering boots are actually pretty good. In fact, for some, they are actually the footwear of choice for continually steep routes like those on the North Face of the Doites as they provide masses of ankle support.
I hired some skis for the approach when I did the Chere Couloir on Mont Blanc du Tacul one year and I had no problems at all ice climbing in a pair of Scarpa Denali.