I think it's time to backpedal RE rock splitting.
I dug around the rock until I uncovered a mass about the size of a card table, and I don't think I've reached the end of it. Attaching a strap again got me nowhere. I decided to take out my rotary hammer and see how hard it was to drill. The rock is very strange. In some places it's like flint, and in others, it's like sandstone. Anyway, it doesn't take too long to bury a 1/2" bit 18" long. I also tried a chisel bit, and because the rock is so brittle, even the hard parts carve readily. Really weird.
Because the rock has relatively thin parts that stick out in various directions, I think splitting it is a viable option. I wouldn't be left with a huge cracked more or less spherical rock I still had to dig out. I would have odd shapes that aren't hard to put a strap on and pull out.
I am surprised to find out how much energy a big tow strap can store. First time I tried to pull the rock out, the strap came loose, and the end sailed right by me.