Random, Frequent, Bizarre, & Prolonged Connection drops (Wired + Wireless)

I don't know. Just trying to think of some cause for three different modem/routers to work fine for a short period and then start acting "weird" and getting worse over time.

I would try that. If you get tech support for one of the modem/routers that will likely be among the first four or five things they have you do.