Pastorp:
I was stationed at Fort Richardson from '75-'78 and grew tomatoes, but not easily.
Find the shortest production time seed you can find (~55 days is the lowest I've seen lately), start them in some kind of hothouse/cold frame, transplant to some kind of hanging thingy and bring them inside if they're not finished producing by frost.
We mostly used 5-gallon buckets with holes drilled in the bottoms, hung from a wire strung up in the basement under a growlight. I used Porter and Black Cherokee seed and they worked out fairly well. Since my wife doesn't look at this site, I'll also confess to experimenting with some of her old pantyhose as a hanger thingy. That worked pretty well; wish I'd had the foresight to market the idea of the "topsy-turvy".