To me, it seems given the right area it could make sense.

You can BRRRR the deals that make sense and sell the rest.

Your input on parking makes a lot of sense. 

And, even then, hitting your rate target would still be extremely challenging unless you were paying points up front, in which case it would probably make more sense to just try to put in a bigger down payment (or pay down the balance if refi) instead and get better terms naturally offered at the lower LTV.

If I can park the 388k ($415-27k) for one year at CD rate of 4.5% and then est 300k (after paying cap gain/depr recap) at 3.0% (assume CD rates lower) that interest income of about 24 months net of ordinary income tax is about the same as my current mortgage.Trying to play devil's advocate and think why selling this year does not make sense. 

So your 35% operating expenses makes sense and seem plenty conservative to me.  

The appraisal was the longest hold up but the junior loan officer we were assigned seems to have zero idea what he is doing and zero sense of urgency...

Either way the numbers can still make sense.

However, if we paid for the house mostly in cash, does it make sense to refinance and incur a high monthly mortgage payment? 

"I have a very simple criteria for when an area is gentrifying as opposed to just generally improving: If it makes economic sense to buy (at market price) and tear down an existing structure in order to build and immediately sell a new building, then the area is gentrifying.