I'll have the home owner check the pins on the lamps.
The AM signal is perfect on all channels. The FM is equally bad on all channels. It sounds like static. It isn't a buzz or hum.
As to loose leads, they would have to be in at least three fixtures - one on each switch. It's a lot harder to get the home owner to check that. I missed my opportunity.
How far away does this affect a portable battery powered FM radio?
A very narrow or fast rise pulse can produce carriers all over the RF spectrum spaced at intervals twice its fundamental frequency. Lets say the pulse rate is 20 kHz (very possible for an electronic ballast). You'd get carriers every odd multiple of that. Both AM and FM demodulators would be outputting a 40 kHz signal. With AM you just would not hear it, assuming it even gets past the narrow bandwidth I.F. filter. With FM, the bandwidth is much wider to cover the wide modulation swings and the corresponding multiple sidebands that produces.
There are two ways this can affect FM. One is that the squelch circuit is being fooled to think a signal is present between stations. The other is that right on a station, the multiple carriers together actually look like phase modulation (which is very much like frequency modulation). If the pulse frequency is very unstable, its instability can come through as white noise on the FM receiver, whether tuned to a station or to an empty frequency. Instability of the pulse rate would actually be good in most cases by eliminating intermodulation with other RF signals, and that may be present in the ballast for that reason (without it, it can be serious source of interference to the aircraft radio band).
If this bad RF is radiating on the power line feed to the lights, then this RF can be blocked at that point with an RF filter. Ham radio ops wire up their own by passing all conductors in parallel (e.g. don't split out the NM) around a toroid core a few (3 to 8) times (need a large core to wrap NM in through it). An inspected installation may need a listed RF suppression device.
It might be possible to do this filtering inside the fixture using the smaller wires (parallel all of them that go to the ballast) so a smaller toroid core can be used. This would likely void the listing of the fixture, however.
If it is radiating through the light bulbs directly, a grounded wire mesh might be needed to cover the exposed side of the fixture. This is unlikely, but possible.
The RF would have to be in common mode to radiate on the line. In common mode, it would not be affected by a capacitor between conductors, or even to ground (where ground is carrying the RF, too). Induction in common (e.g. all wires parallel in the inductor) would be what would block it.
The ballast is definitely bad if it is leaking this much RF.