Cuben fiber tarp hung on bias.

Cuben will stretch in a direction 45/135 degrees to the reinforcement. You can do this with your fingers without too much force. So, if you plan to orient your tarp as you described, you could minimize tensile forces on the material parallel to the ridgeline by affixing the ends of the ridgeline (the corners) to a taut support cord that runs underneath.

An alternative to Colin's suggestion of using cord would be to run a piece of 1" cuben tape from corner to corner. Then there will be axially aligned fibers running the length of the diagonal ridgeline which should take up the force. MLD does this on some reinforcements for their shelters (e.g. for the door on the Trailstar). Ron or any of the other cottage guys could probably add this for you as an option for cheap to a new 8×10 tarp order.

Alternatively there is a version of cuben that is made with fibers at 0, 45 and 90 degrees which would be full-strength along the bias.

I like the tape idea. I would have never thought of that. I'll check out the trail star and see how it's done. Thanks for the assistance guys!