In the wild grapes also smother out and strangle trees ultimately killing them. I do not grow muscadines, but figuring they are similar to wild grapes I'd say it's a no-go. Grapes are prolific growers and like any plant will search for, and ultimately obtain, the best light depriving the structure plant of the same.
Behind my home is the largest assemblage of wild grapes I've ever seen (and I grew up here) and dead trees and broken branches are everywhere in their wake.
You are looking for the lazy man's, easy way and I don't blame you...we all are, but there is a reason people grew them on arbors and trellis's for centuries.

Just ante up and build a proper structure. If nothing else an existing old fence with a little added structure will function well and is low enough to make harvesting and pruning easy and efficient.

Maybe musky's are different....I doubt it.

I am absolutely looking for the lazy way. However, it is also a matter of space. If I can't grow grapes on the tree, I'm just not going to grow grapes at all; I'd rather use the more prime real estate for something else.

How do vines "strangle" a tree? If I were willing to prune it back every year, would that suffice to protect the tree? I certainly understand sunlight competition, but pruning should be able to prevent that. I'm not wedded to the idea of muscadines, either; any fruit vine that is resistant to disease would do.

There are plenty of examples of growing grapes up trees. Folk practice in Italy used maples, which were most likely pollarded, or cut back annually.

Mark Shepard, and Sepp Holzer, two permaculture farmers also use trees as supports for grapes.

The main issue is getting enough light through the canopy of the tree to get your grape vine to produce. Pick the sunny side, if possible. You'll also need to prune your vine to keep the eventual fruit within reach.

I've been planting locust trees along side the cedar posts that support my grape trellis presently. In four or six more years, they will be ready to take over, and my cedar post will be needing replacement. Locusts will fix atmospheric nitrogen, and release it into the soil as they are pollarded while providing bee forage, and greens and seeds for my chickens-that's better than PT lumber by a long shot!

You can do it but don't let them reach the top of the tree. Wild grapes in my area grow until they reach the top of trees and then spread out over the top killing the tree.