OK - I'll answer my own question.

Thanks to a video on youtube (https://www.youtube.com/watch?v=yRRcLVNqgC8) I learned there is a chunk of wiring over the final (3rd) screw.

I used gorilla super glue on the worm gear. I roughed the shaft of the motor up good, first. Be careful - that stuff sets up FAST and you need to align the worm with the keys that make it turn (they protrude from the motor shaft).

When I took the thing apart most of the mickey-mouse plastic thingys that hold the two halves of the cast together broke - old, and brittle. A single tie-wrap (cable tie) fixed that.

Put it back together - motor does not run. Turns out the case interferes with the outside motor contacts. Bent that, worked fine.

Test the thing before you install it. Just let it hang on the wires. Start it up and watch as you move the temp knob. Make sure it works...

Finally, after I installed it, it would not work. Had a hunch. Disconnected the water valve cable (on the firewall, dead center). Then it worked. Sprayed copious amounts of blaster on both ends of cable. Helped it with vicegrips under the hood. Now the thing works.