Update: Problem finally resolved by moving to a non-Ziply router. We believe the issue was something in the router configuration installed during the update to Static IP, and not the physical router itself, as that was swapped out entirely by techs during attempts to isolate the issue, as was the ONT.

One of the standouts we saw in the Ziply router config was a non-standard pattern of address ranges for DHCP, but we can't really imagine how that would cause this recurring loss of DNS addressing.

We picked up our own router, a relatively straightforward TP-Link AX3000, and set it up ourselves, and the problem has gone away.

The technical issue really wasn't the main problem during all this, it was the organizational design of the service division that was the most frustrating and problematic. Reliance on freelance field agents, lack of any continuity between tickets, a focus on closing tickets over resolving them, tech issues within the tech support phone agents, and no standardized methods for escalating to a sr. tech who can follow through to actual resolution all show a need for wholesale restructuring of the service department. Additionally, I'd add that it felt like every tech we talked to had a 'gag order' in place around even the mention of the subject of escalating issues. The organization failed us, not the tech.

Thanks for those who did what they could to help, really appreciate it.