Okay, thanks everyone for the help so far. I broke down and got a WNDR3700, then configured it as an AP to replace the one in my family room (still using the stock firmware for now). When connected to it using 2.4ghz, I still see the same problems as I did connected to the WRT54g. However, when connected to the 5ghz network, everything's smooth sailing. So, my problems are more or less solved.

However, I've got a couple of more questions:
1) Is there some way to configure the 5ghz side for a more seamless roaming experience? Since only one of my APs has been replaced, the other 2 are still only 802.11g, and I don't want to run in to any problems where I'm getting poor connectivity at the other end of the house because the computer's still trying to connect to a 5ghz 802.11n network that's no longer close by. If I set the 5ghz SSID/password to the same as the 2.4ghz one, is a laptop supposed to just be able to figure it out the same was as it does when roaming between the other 802.11g APs?

2) Just for fun, I still want to figure out what's going on with the 2.4ghz side of things. I still intend to get some other software to analyze the other networks in the air, but in the meantime, I'm using the new built-in wifi scanning stuff in OS X 10.8. It's showing no obvious problems with my own connection in terms of signal strength or noise, but yet I still have problems. My symptoms are thus: In this one room of my house (the family room), I have intermittent connectivity, yet the computer shows full signal strength at all times. If I ping the AP, sometimes I have sub-millisecond ping times, sometimes it's more like 3-4 seconds. If I let a ping run for a while, I'm apt to lose about 20-30% of the packets. The packet loss is highly dependent on the orientation of the computer. Facing north is much worse than when I'm facing south, for example, and placing my hands in strategic spots around the computer can mitigate the problem. It's also highly dependent on the time of day. I usually have no problems during the day, and many problems late at night. It's not constant, though. I might struggle with it for an hour, but the next hour it's just fine.

So, what's your gut feeling about this? Interference from too many other nearby networks? Or, do I have a neighbor who's building a supercollider in his garage or something?

(For future reference, I've tried it with every other part of the network off/disconnected except the one AP. I've tried turning off every phone or anything else that might be in that band. I've turned off every fluorescent light in the house, even pulling a couple of breakers for lights where there still might have been electricity going through the ballast. I unplugged fridges and freezers and things with motors that might have been sending some electrical noise through. I think I covered most everything that could be environmental in my house.)

I'll be back later with info from scanning the nearby networks to see what's relevant there.