Fascinating adventure. Oddly, we've probably got too many clues right now, but the most intriguing one seems to be that the carriers switch on and off together.When you mentioned being so close to a 230 kV transmission line, Glenn, I was immediately inclined to assume PLCs were the origin; but if some of them are go/no-go status indicators, they should come and go at different times. If one of them is doing data polling, it seems it should appear first by a few moments, and the others ought to respond perhaps in some sort of sequence.
RF-ballasted lights can certainly be responsible for squirrely QRM as Bruce mentions. The on/off together problem could possibly be accounted for if your neighbor has a very large room in which all the lamps and fixtures (likely containing bulbs from multiple sources) are activated by a single switch. You could watch to see whether one end of the house or another seems better lit while the mystery signals are present. Same could be said about a master power switch on an entertainment center, activating multiple SMPS units in TV sets, DVRs, Blu-Ray players, etc., simultaneously.
Inverters of the kind found in EV fast chargers, home solar power systems, community-size battery power storage facilities, and similar installations could conceivably cause similar effects.