I'd like to build up some equity, but I'm struggling to find value-add properties (and get offers accepted).

Avon, CT is a hot market, with multiple offers being received the weekend of the open house, which is scheduled one week after listing.My offer of $725,000 was $20,000 lower than the highest bid, but was accepted without counter because it was not contingent on financing, while the highest offer at $745,000, while the buyer had pre approval financing, was subject to financing.

What is a fair offer to make to that GC, and what kind of deal should I not accept?

Make enough offers and often times you'll suprise yourself what some ppl will accept some times. 

Even a contractor with 30+ years of experience only knows what they know - so, they may not know the most cost-effective solution:(5) Political trends that may lead to more controls on landlords - being forced to accept S8, not being able to deny for evictions, rent control, etc.

It was suficient/accepted by the lender that granted the mortgage for the duplex, so I did not anticipate running into this issue trying to get the heloc.

However, the seller decided to hold off on accepting my offer since the property had only been on the market for 7 days and they wanted to entertain other offers.This experience made me realize the importance of paying attention to the number of days a property has been on the market.

Are you saying DMM is acceptable because other methods CAN fail too?

Tenant can still pay rent, late fees, and other penalties in full and get back into my good graces, but I do not waive any fees, accept payments, etc.

We didn’t accept the payment and requested proper payment.