I'm no expert, but I would personally feel VERY uncomfortable cooking in any tent, especially the firstlight. I owned the lighthouse a while ago, and while I really have no clue about the flammable properties of Epic fabric, I'd bet it would go up in flames pretty quick. If it's so windy you can't cook outside a tent, imagine trying to stay warm in those conditions after your tent has gone up in flames.
Another reason I would never cook in a tent, especially in Alaska, is that the smell will attract animals. You would not be able to see animals approaching, and even if you did finish your meal uneventfully you would then be sleeping in a tent that smells like food. A squirrel trying to chew through the fabric and get in would be bad enough, not to mention wolves, coyotes, black bears, grizzlies, and who knows what other kinds of animals.
I would never recommend cooking in a tent. No matter what you do to make cooking inside your tent safer, their will always be a potentially life threatening risk.