Quite the essay you have written. That you have a home (non-)warranty, and
faith in the BBB as a quality detector, shows that you have much to learn.
Those two things are prime indicators for "sucker". But my hunch is, you
got suckered on the house itself.

Offhand it sounds like you need to renovate with a zoned hot water system.

A different house might be simpler and cheaper, if the process was informed
by some critical thinking.