After expenses and mortgage, I end up with a net cash flow of anywhere b/w $150-$250 which I find rather small, and I wonder if this could even get eaten up by tax filing time.

South Carolina, specifically Greenville, is often pretty attractive to us just over the line in North Carolina, but keep in mind that as an investor you'll pay MUCH higher property taxes there. 

Is it worth waiting until September and hope the market is still as strong or take the hit on capital gain taxes and sell now.Secondly, if we do hold this property would it make more sense to prioritize debt paydown (instead of investing in another property, put our cash towards our mortgage payment and have it paid off within 10 years.

There are also tax issues. 

I am looking for best practices both from a legal protection standpoint and from a tax advantage standpoint.

There would be no way for you to prove that this claim WASN'T true, unless you followed a more rigid protocol and documented it. 

For property owners with out-of-state investments, is it necessary to keep all receipts and invoices for write-offs during tax season, even smaller jobs performed by the PM's handyman?

After taxes I am ending up with roughly ~$6m.

As long as you have positive cash flow on debt that is tax advantaged you are not over leveraged.

The home has no liens and is currently behind in property taxes by 1 six month payment which was due in February.