My first thought is that it is a signal strength issue, probably too strong a signal from the ONT. I have never experienced that directly, but when I started getting a few channels that occasionally would say "currently unavailable" I removed the attenuator that the Verizon installation tech had put on my DVR and bingo, that fixed the problem (the signal strength supplied by the ONT had apparently dropped some over several years to cause this). That is exactly the opposite from what I guess your problem is, but I have seen many reports about pixelation on Tivos with a signal that is too strong, and putting attenuators between the splitter and the Tivo fixes it.
If you see a Verizon truck in the neighborhood flag him down and ask for a couple of attenuators of different DB values and try them out, it might just fix the problem (or did any of the techs that have been to the house try adding any attenuators?). Or if Verizon does send a tech out again, ask about trying attenuators.
Verizon FiOS TV, Internet, and phone
IMG 1.6.2, Build 08.58
Keller, TX 76248