I replaced everything downstream of the drop from the street, all new wiring inside, a new modem/router/etc. All signs pointed to the problem being outside the house. I went so far as to connect an oscilloscope to the coax line to look for patterns. I discovered that if I physically manipulated a particular section of the line from the pole, a huge interference pattern appeared and the modem's connection dropped. Eventually I could reproduce the connection loss fairly easily.
Convincing the ISP to actually do anything about it was much harder. Despite first-hand evidence that the coax from the pole needed to be replaced, their tech support insisted that someone had to come into the house to inspect the interior wiring. No amount of insistence on my part would convince them that it was not necessary. The building was a vacation home, and this was during peak COVID time, so there was basically no chance of that happening. The appointment came with threats of service charges if they sent a tech and could not enter the building or reproduce the problem, so I cancelled it.
Coincidentally, I happened to discover that the mayor of the town had started a hotline specifically for reporting home Internet problems in the town. So I sent in a message to that service, not really expecting anything to come of it. But shortly after I get a phone call from some higher-up department of the ISP. They had a truck out within a few days to replace the drop -- with no one home -- and the connection was rock solid ever since.
This experience taught me that ISPs often have distinct support channels that governmental departments use to contact them. I think they called it the "executive support team" or something along those lines. Basically, if you can get a message in that way, it's possible to circumvent the useless consumer-level support. Long story short, I think escalating this through the local or state level government may be the author's best shot at getting this resolved.
I should clarify that I didn't really do any _true_ diagnostic with the scope. Simply as an attempt to gather as much data as possible, I connected the oscilloscope to see what the signals looked like. And, because, why not. I had driven 2+ hours to get there, might as well try everything! I didn't expect it to actually be able to decode the signals. I was surprised to find a correlation between the modem losing sync and a visually-distinct pattern appearing on the scope though.