That's a really creative idea. You folks in Alaska must know an awful lot of tricks that the rest of us in the northern states could benefit from.
Are you growing an early maturing variety of tomato? I'm thinking that you might get the same benefit (or maybe more) by covering the soil with black plastic after the soil warms up. Black absorbs heat from the sun (as opposed to reflecting it) and the plastic keeps the cooling winds off the soil. Watering is the complication involved, but the plastic will also retain moisture. I'm just thinking out loud... err...out fingers
Staking the plants will surely help.
I tried the black plastic but got lower soil temps, I found that clear plastic let the suns rays pass to the dark colored soil & heat the soil. I got about a 9 to 12 degree soil temp gain (4" deep in the soil) on clear plastic over black plastic. That is one of the reasons I made the box with GH sheeting, to let the heat get into the soil & hold it in a little longer into the night.
Pricy tomatoes for sure. But so are the ones i grow in the GH. But the flavor of a vine ripened tomato (for me) is worth it.
I've been trying to get good flavorful ripe tomatoes outdoors here for years. I had my best success lat year with this box & the "4th of July" hybrid. A few ripe tomatoes with some flavor, Not as flavorful as the same tomato in the GH but some tomato flavor.