I love your neighbors story. What you actually could have done is is broadcast on the FM frequency with very low power they were on and cause capture effect to take out there signal. If you wanted you could have hooked up a mike and told them to turn it down. They would have freaked
I had neighbors years ago that the parents weren't home and the kids were throwing a very loud pool party. That had music blasting so I transmitted with a FM micro transmitter and fed Classical music from my dish on that frequency. Very fast the radio went off and stayed off.
I like the classical music idea. That would have freaked them out (ie to get the same classical station no matter what channel they tuned to) even more than talking to them, plus I didn't want them to know I was doing it, because I had already had concrete blocks thrown through my car window, and a dozen eggs thrown at my windows, and numerous other vandalism episodes every time they decided that they didn't like me. But the classical music thing might have been a life altering experience for those neighbors.
My generator only had AM modulation, however. I think I may have tried switching on the built in AM tone, but I can't remember if that came through or not. I don't know if FM micro transmitters were readily available back when I did this (back in the late 70s). I wasn't technologically savy enough to put together a FM transmitter from scratch, although I might have been able to modify the signal generator to introduce FM modulation.