I didn't hear from anyone who actually had done the repair job themselves. I made two decisions. I will send the module off to Victor to have it repaired. He has plenty of solid recommendations and, considering what he is doing, the price is reasonable. (Victor, why do you do that convoluted Ebay thing? Isn't there a better way that costs you less and is easier for those not registered on Ebay?)

Secondly, I will have a quick shot at fixing the module in the interim, since I have to put it back in the car for a state inspection. So I got out my thickest magnifying glass and my 200W halogen lamp and looked again. There were a couple of marginal solder joints: a little brown residue under the joint; a not quite covered enveloped wire. Still, there was nothing that yelled out, "Joint failure!"
So touched up a couple of the joints the best I could and sealed up the box. (I did not put a coating on the board again, since I expect to take it out again in a couple of weeks.)

I put it back in the car and drove over a bunch of potholes and speed bumps with the brakes partially applied. (This always triggered the fault codes and ABS/TRAC lights.) Nothing. I drive it out on the road for about fifty miles, since I'm also trying to get that d%#--ed OBD system to set the READY flag on six of the I/M systems.

Thus far, I had no codes pending and no lights on. I will still send it off for repair as planned. I hope Victor lets me know exactly what needed to be fixed.