Matt, I finally got the chance to test out the entire high-draw breaker box and apparently identified the circuits that are generating the problem. It's two doubles and a triple that run, in order, the garage door motor, the garage dehumidifier and the heater pump. The one that seems to have the quickest effect is, oddly enough, the garage door motor breaker.
I'm really happy to have apparently narrowed it down. Now my main concern is: What the heck can I do about it? It's not as simple as installing a FilterLinc in an outlet, since the garage door motor appears to be wired directly to the breaker box and appears to have a much higher draw than a FilterLinc is designed to handle.
Another small couple of issues: First one: With the offending breakers off I can send an "All Lights On" command and it will work flawlessly 95% of the time. There's bound to be a couple of errors here and there which I guess I could live with. When I send an "All Lights Off" command the same devices I just flicked on will respond, but VERY slowly and with noticeably greater number of errors. In testing today it took over 3 minutes to turn the whole house off, while it took maybe 15 seconds to flick it on. However, if I issue the "All Lights Off" command a second time, everything will flick off in seconds. Noise again? Unbridged phases? The house has at least 7 devices per floor, none further than a few feet from the other and no further than 10 feet from devices on other floors. I assume if it's not repeating well over the power wiring, it should have no problem repeating over RF.
The other one: I have one device, a KeypadLinc Dimmer that has refused to be found all but once, with all the high-draw circuits off. I naively thought it would be easily found again if I deleted it it and re-added it to test the network there, but never could. The odd thing is once it was found it would respond to on/off commands, physically turning the light on and off, but it would always report an error. Odder still is that it's in the same room as two other KeypadLincs which work perfectly. One of them is a few inches away from the one I can't seem to get Indigo to talk to.
Thanks for all your help!