So today ozone treatment and air return box repair, then I found some dry but soft base board behind the refrigerator

Wait til something blows up and they get in court on just about any issue and learn what they thought they were was not at all what they were....LOL

For example I'm thinking of David Greene's suggestion that you agree up front to provide a monetary incentive for the GC to get the work done correctly and on time, along with a penalty for blowing past the deadline.

If you interacted with persons in trying to understand there quoting as you communicated here, no you wouldn't get much for answers because it's demanding, condescending and with hollow threats, nobody wants to deal with that BS or person so of course they blow you off, I bet you'd blow that person off too. 

Is there a world where it makes sense to leave parts of the dry wall up and try to just clean them?

We put a lot of efford and attention into keeping basements dry, but we still have an occasional pipe burst or sump pump fail and see issues and when you get water in a basement; carpet can be dried and cleaned, it's the open cell pad that is holding on to gallons of water like a kitchen sponge.

Better yet is to buy well so you can pull as much of your own money out as soon as possible to replenish your reserves and have dry powder to put to work for the next deal.

My international bookings, which usually comes from Booking com, have completely dried up ever since the dollar got real strong against foreign currency. 

I own all different types of real estate assets, a few laundromats, a few dry cleaners, and a payment processing company.

So buying occupied homes is something you want to be careful about.. its not juust cut and dry.