Any owner occupied loan would work FHA or low money down conventional.

I don't want to sell until I've used all my tax credits, and I don't want to do a cash out refi because of my low interest rate.

There are far too many hungry loan officers (No offense) trying to make it in the business who are never closed on a commercial loan of even A DSCR loan.The problem with that is it will cost you lost money and most importantly lost time!

I am here in southern California and homes are still selling in less than 2 weeks.The agents that price the homes correctly will get multiple offers and sell in less than 2 weeks.The agents that price the home extremely low for marketing purposes will get 20 offers on a home.I tend to price the home slightly higher than the market and see if any buyers will bite, if not we typically adjust the price down over a course of 30-60-90 days down to the price where we start to get showings and offers. 

Some have heavy appreciation but lack cashflow, some have high taxes, low taxes.

Now of course if you are buying in the low-income areas, you BETTER have a trusted team in place and you too need to know what you are doing, 

Are there Hard Money Lenders that still do Gap Loans with simple underwriting and low origination fees?

My lender just informed me that my seller concessions exceed the relevant closing costs (including points buydown) and that the money left over will be a “wash”.

At 6.41% your refinance is not really gonna help you and I would only refinance if you are in it for the long haul due to the costs of refinancing. 

Just so you know on my newest purchase I am looking for renovation money as well as financing and the bank is looking for formal quotes as to the materials needed and the amount/cost of the labor that will be involved.