Why does my 1997 Chevy Suburban drop out/not shift after 2nd gear?

On a trip today we were driving down the Interstate when all of the sudden the RPMs went way up and we lost all power.

We managed to get off the road, and some experiments, at 25MPH it would basically shift into neutral if it was in (Over)drive or 3rd. In 2nd gear it would stay in gear, just keep increasing RPMs. At one point I was in 2nd gear, heading up a hill, and shifted it into 3rd and it actually shifted into 3rd, but it was probably around 3-4k RPMs at that point. It did stay in gear until I let off the throttle.

We thought it might be the speed sensor but… well, we just replaced that and it’s still doing the same thing. I did notice that the plug was pretty oily, I’m not sure if that would do anything.

Any clue what’s going wrong here (and more importantly, how much I should expect to repair it)? I saw a couple of things that talked about something called a sprag, or some sort of solenoid, but I’m not sure if any of those apply.