All good info. Snowshoe bindings are much more forgiving than crampons, etc. They'll fit most any footwear. I snowshoe all the time in my Scarpa T1s, with no trouble. I like to have them for the ski down, and I don't like backcountry boot changes, although the chemical heaters are a good idea.
A lot of it depends on your specific alpine ski boot, if that's what you're wearing. Regarding the walking, some boots have a better "walking release" mechanism than others. Any leg fatigue you get from hiking in the ski boots is more due to fixation of your ankle (so you don't toe off) that it is due to the weight of the boots. Regarding getting into the boots, if you do decide to change, that also depends on the boot, and whether you keep it warm. About 25 years ago when I was still skiing alpine I had a related experience. When I got to the summit, I was unable (even with the help of a partner and two ski poles) to force open my frozen alpine ski boots to get them on. I ended up skiing down with my plastic mountaineering boots force fit into my alpine ski bindings (doubtless an unsafe set up).
I'd wear the ski boots, keep them loose, and wear a gaiter to keep snow out of the loose tops.
TCD