This is a complete long shot, but this quote:
But, this reminds me of something my tv station engineering pal said. They did a a software tweak a few weeks ago, not affecting signal strength.
Did that happen around the same time you lost the channels? It reminds me of something that happened to me with Windows Media Center several years ago. I had a local OTA station “disappear” - I think it was still in the WMC guide, but I couldn’t tune it or record from it. (It was a while ago so I can’t remember the details offhand.) But the TVs I had hooked directly to the OTA coax could tune the channel fine.
At the time, I did some digging online and found some sites that eventually helped me figure it out. It turns out that the station had done a software update and had something misconfigured in the ATSC stream metadata regarding how the channels were defined. While it was technically wrong per the ATSC spec, a lot of tuners (i.e. all my TVs) didn’t care, but WMC was “picky” and when it saw the metadata was wrong, it just threw up it’s hands and decided that it wasn’t a valid channel.
I don’t know if this is what’s going on with the Tablo, but maybe it could be the same or similar issues. Since this was a while ago, I unfortunately wasn’t easily able to find any relevant bookmarks or emails, but if this seems plausible, let me know and I’ll see if I can dig out any more details from my archives.