There are other ways to get your offer accepted that can be appealing to the buyers like non-refundable deposits, higher deposit amounts, shorter timelines and others.

I would say no - that a PO box is not acceptable for rental history.

As part of the payoff, I accepted the title to the empty lot that was additional collateral for the loan, and leased it back to the church for parking at a 12% 3N annual return.  

Or if they continue to be difficult to work with, start looking for a new property manager.I don't think it's necessary for you to specifically mention in your listing description that you accept section 8 tenants because it's illegal to discriminate on the basis of income in Illinois, which protects Section 8 voucher holders.

For example, I mention that every adult must pay a $30 application fee, pass my credit/criminal background, make a combined income of 3x the rent, and whether or not the property accepts pets.

Or should I take the risk and trust that if I refinance now, accept the lower cash flow long term for this rental, and then use the freed up HELOC to get another investment sooner (maybe this year). 

This happened because carriers are no longer accepting 10DLC campaigns related to real estate.

But if your goal is to earn tax deferred income and appreciation you can pass to your heirs tax free you can accept less. 

We feared it was too low, but we were not willing to accept anything more and left it in Gods hands.

Like any state or federal government, something happens and they swing way to far in the other direction,I applied for licensing in california and they will not accept federal fingerprints.