Everyone I've talked to just bolts the skiis directly onto the bottom of the sled. I was surprised to learn that this alone greatly increases the things "flotation" on snow. I am, however, referring to more sledlike portables...like fish traps. Don't know if you have to remove the skiis in order to set up your frabill.
If a permanent bolt on solution is not good for you, my suggestion would be this:
Bolt a 2x4 onto the ski, with the 2x4 on its side. Sink a couple eye-bolts into the side of the wood, and clamp/strap the hut onto the rig. this way the whole thing is off the snow, and it just unclips from the skiis.
Oh...don't know how wide your hut is when collapsed, as per your pic, but what about getting a Jetsled? Used ones are often easy enough to find, if you know the right person (ahem...I may know somebody )