I'm going to answer the first part of my own question.
After upgrading my iPod Touch to iOS 5, Location Services started working again. Not only did it start working, it's showing the location as a point in the street in front of the house.
1) The location I manually submitted to Skyhook in 2009 was in the street farther south, by the mailbox, so the old data point is not being used. Not suprised since I have no reason to believe that Apple went back to Skyhook. A visit to Skyhook's website verified that this point has not changed.
2) The location that Apple started using last year was a point on the main highway 1/2 mile east of here.
So somehow Apple has independently obtained new data about my wifi location. It's possible that during a recent party, somebody with an iPhone had connected to my Wifi and that data was sent back to Apple. It's also possible that a Wifi data collection vehicle drove down this road. It's very rural with only three homes on a one mile stretch, so although possible it's difficult to believe.
It was my previous understanding that Apple started requiring that devices be within range of several Wifi signals to improve Location Services accuracy. Being in a rural location, it's nearly impossible for my iPod to pick up any Wifi signal other than my own. With Skyhook, this was never an issue.
However, iOS 5 seems to heavily depend on Location Services so maybe they've changed something critical to how it functions in order to improve accuracy without requiring multiple Wifi signals.
I'm going to accept my own answer. If anyone has a better answer to my original question, I'll consider accepting that instead.
Best Answer
It turns out the only thing to do is wait. I called Apple and the rep said that if power cycling the phone and "forgetting" the wifi network didn't help, the Apple database would clear stale entries after 30 to 60 days. Sure enough, after about a month my phone started showing the new location.
(Note: I tried @bmike's procedure several times on each of the iPhones in our household, but it didn't seem to make a difference. It could be that the procedure does remove that phone's historical location info from Apple's database, but over the many years we were living at our old address we had enough guests with iPhones that removing only our own phones' records wasn't sufficient. If anyone else is having this problem you might as well try that procedure, but know that the problem will self-resolve within a month or so.)