OK, update on my problem (it appears that it was NOT fixed by strengthening solder connections).
It worked fine for a week or so, but then one day going to the airport (on a very humid morning after sitting for 3 or so days), it went all goofy and went out. Pressing near the #3 did bring it back, which still suggests a problem with the front panel.
So, perhaps I wasn't clear enough to the TV repairman that he should check the front panel. In this thread, fod1 suggests a different solution:
http://www.subaruoutback.org/forums...ectronics/36519-stereo-ac-systems-blinking-going-off-randomly-2008-outback.html
So, I pulled stereo back out, and unclipped the front panel. Sure enough, there were 4 fairly weak prongs that must make the ground connection between front panel and case. I couldn't tell how weak the connection was, since in order to see them the panel has to come off. I bent them out, and put some dielectric grease on them. I also wonder about the multi-pin connectors in the center, near the CD tray. It would make sense that pushing on the #3 would strengthen that connection. I didn't know an easy of making that connection really strong.
I tried tightening the screws that hold that circuit board in place, in hopes that it could pull the board forward and tighten connection. Also, there are 6 screws that hold the front panel to the radio, and it seemed like there could be some slop in those screw holes that I could use to my advantage. So when putting the front panel back on, I pushed on the front cover kinda hard (especially near the #3), while tightening down all the screws. Hopefully that pushes the cover back.
I then took the car to some rough washboard/gravelly backroads and pushed it a little hard for a while, and no blinks or hiccups from the stereo/hvac.
In any case, I'm still not sure if I fully trust the stereo for our week and a half trip to Maine next week. My wife decided that we should buy a second stereo/hvac unit off ebay and keep it with us as backup. If we don't need it after a month or two, then I'll sell that one on ebay or to a forum member (perhaps after strenghtening all connections like I did with the other one, just so its better than factory). That stereo should arrive today.