[fsammartino]

I also want to add my thanks for the $900 this thread saved me!
I'm a bit of a novice, and was unsure about some things even after thoroughly reading the posts, so here is a little summary of the steps for other non-mechanical types like me. This is the situation for a 2003 Highlander:
1) the "bezel" - refers to the large plastic piece that goes around the heater controls and radio, and includes the 2 vents (grills and all!) on either side of the heater controls. I started from the bottom where the bezel is narrowest and easiest to grab, and slowly pryed and gently pulled it out. I used a couple of those cheap disposible plastic putty knives for the hardest part around the vents on top, until it had come out enough to grab with my fingers and evenly pull out the rest of the way.
2) remove 6 bolts, and 2 screws from the aluminum brackets on the sides (also pull apart the aluminum brackets enough to get past a couple of positioning posts), and the whole heater/radio unit pulls forward enough to easily remove the 3 connectors plugged into the back. The heater unit then comes out complete with a plastic bezel piece that goes around the radio
3) 8 screws and the back cover comes off the heater control unit.
4) I pulled off the knobs only after I had the whole heater unit out. My heater control was so loose that I was afraid I'd break it when I had to force the knobs off. But the knobs do pull straight off - I used a couple of small screwdrivers on either side for leverage to gently and evenly pull off my loose knob
5) the soldering was a little tricky, because the wires are small and close together. Use 24 or 26 guage stranded insulated wires for the patch job, along with a sharp-tipped soldering iron. I used a wet spong to clean the hot iron tip each time. Also it helps to first melt a drop of solder into the bare wires at the end of your new jumper wires. That makes it solder easier and quicker to the circuit board, so you minimize the amount of heating you do to the circuit board.
6) the whole operation took me 2 hours, but I could probably do it again in 1/2 hour now that I know what I'm doing.

Good luck and thanks for the tips everyone!