Pete --

"...possible that turning the heater on full would change the dash temp enough to "warp" that board or its contacts so that a normal reading is at least temporarily returned..."

Gosh, I don't think so. That would take a substantial temperature increase.

In your shoes, I would first resolder the compensating board, and clean and tighten the pin contacts. One trick is to twist each pin 30-45 degrees so the edges of the square pin will now "cut" into any oxide coating on the contacts when you reinstall the board.

If you decide to replace the DIP, I have a bag of 'em. They work.

"...don't want to tear into my dash if it's not necessary..."

Actually, yanking the cluster takes about 5 minutes. Removing the circuit board from the cluster housing (to access the comp board) takes another 5 minutes. All-in-all, it's an easy, clean, straightforward job.

"...he digital temp idea..."

I use a hand-held gauge -- Fluke, I think, or maybe from Omega -- and a thin film thermocouple. I think I got mine surplus years ago. However, I see this kind of stuff on eBay going for pennies.
--
Don Foster (near Cape Cod, MA)