Another approach you could consider is to replace whatever bindings
you have on your alpine skis with the Naxo AT binding, get some skins,
unbuckle the top two buckles of your downhill boot and skin up with
that setup.

I was very impressed with the natural stride the Naxo gives you in
climbing mode and just toured with a guy who was in alpine boots and
claimed they were totally comfortable on long hikes on the skis...