@Matthew Anderson- thanks ...good job ...Most  lenders will not  have a cash out refinance  program  that will  have a LTV  above  75% ...you might  focus on getting a rate/ term  refinance done to payoff the hard money loan and cover these costs  and then  try to replenish your remodel costs some other way  ( HELOC on the subject property or on your home )

Then request the draw, replenish the goose egg, and do it again.

You should be able to get maybe 3 properties out of that, and the cash flow from them should start replenishing that savings.Aggressive house-hackingHouse hacking will be a quicker path but requires you live with others.

You can still take some cash to replenish your capital but the cash injection into another property avoids the hit. 

Real estate is the business of time and sometimes you have to let some go by in order to replenish your reserves. 

--simply take personal funds and "send back through" borrower to satisfy the note and replenish the balance. 

I don't like doing it and always replenish the reserves right after closing, but it has happened.

Without a source to replenish it, they don't even get to rent my $1k/month unit.FHA will require your income the same as all of the conventional mortgages will.Best of luck.

In other words, they will effectively and legally add pass through fees on utility services (just the privately owned services) to replenish their general funds. 

When ever you use any of the reserve, you immediately stop taking any of the money and replenish it until it is fully funded.