Hello,
You asked if anyone has tried a tarp over a large area - Well, one of my neighbors has a large Brunswick fig (the trunk is about 7 inches thick) that he has trained very low to the ground. The vertical part of the trunk (if I am remembering correctly) is only about 2 to 3 feet high and then there is a longer horizontal portion. In a way, he is pruning it like the Japanese methods.
Anyway, at the end of the season he cuts off most or all of the 'water sprouts' (current year's growth) leaving the main trunk. He fills the entire cavity with straw and / or leaves. Next, he stretches a large tarp over the entire area and seals the edges by putting bricks all the way around to hold the tarp in place.
Remember this is in Kansas, zone 5 (although not always as cold as zone 5 due to the variable weather patterns). He does not add any heat either - no lightbulbs, heat tape or anything. I think that he has been taking care of that fig for at least 20 years and possibly more.
If I had more space, I would try that method myself. The plywood box was just an experiment and is working for this situation.
Ingevald