Texture-wise, they remind me of a cross between an apple and a ripe pear. They aren't overly sweet -- which I think is good. There is a pit in the middle, which is easily removed.
Neighbor Phil, who also has a neighbor with a mountain apple tree, and who is also buried in mountain apples, had a good suggestion: Juicing them. We own a juicer (Braun brand) which is a workhorse. I think we've had it for about thirteen years. My only issue with it is that it has a lot of parts, and I'm really terrible about re-assembling it. Mr. L has to be called in for that chore. Nothing against Braun; I also suck at puzzles.
So, we sliced up the mountain apples, removed the pits, and put a batch through the juicer. Phil described the juice as tasting like strawberry lemonade. I think Phil has an overactive imagination. (I guess I shouldn't throw stones -- I'm the one who thinks that Poor Man's Filet Mignon tastes like filet mignon). It was pretty good. The color was nice, too.