My purely unscientific and unsubstantiated theory is that it's still an interference problem even though the light is staying off.

Assuming that you've tried different remotes, different base stations and the combination that doesn't work at the house DOES work on your test bench.

Could it be that the radio towers are on completely different frequencies, but their output is so strong that it's completely jamming all other nearby RF?

There's a tower in town here that broadcasts AM at 960Khz, but even if I'm tuned to say....1000 mhz, I can still clearly hear its signal as I drive past it.

Is it possible to throw in the towel and just use a hardwired IR repeater?

Incidentally, I'd be interested to hear if say an RTI or other competitor worked or had the same problems.