OK, everything checks out so far in terms of connections. The only steps I ran into problems with were these...

Set the multimeter to measure resistance, measure across the pot connections and roughly set the pot to 870ohms.

The highest I could get the pot was 763. The screw reached the end of its travel and just clicked...

If there is a sudden burning smell, or you notice anything getting really hot, or melting, or going bang, disconnect immediately.

Nothing blew up and nothing smells funny, but the heatsink I connected to the regulator got really hot. Like burn your fingers when you touch it hot. So I disconnected. I had it hooked up to a car battery charger that was outputting about 13.98V. I also tried it with a 9V battery, and it got kinda hot that way too, but not as much.
Maybe I've got the regulator hooked up incorrectly?
See edit in next post

The switch works fine, and the LED works fine.
This is the potentiometer I got and this is the regulator.