My first thought is that there's no rule book on what bindings you have to mount on certain skis. While someone might think it's silly to put a Dynafit on a ski with metal in its construction, I don't. Sure, it's going to be a little heavier on the ascents, but since you're planning on relatively short excursions I don't see that being a big issue. You'll get more stability on the descents, and let's be honest most of us only go up so that we can come back down. I personally have never focused on weight savings when I put together a touring setup, I focus on what terrain I want to ski and what's going to be the most fun on the way down.
I think the biggest argument against it would be that you'd lose some precision in terms of the skier to ski interface. You probably won't be able to take advantage of the full torsional stiffness of the ski if you were, say, trying to arc Super G turns on firm groomers, but that's kind of a moot argument for a ski that's 105 mm underfoot.
I say go for it!