Ready to BRRRR into my 2nd investment in Tucson; refi first?

[Holly Boss]

This is probably a question to ask a lender but here it goes: I'm about to refi my investment property to buy a second investment property which also will be a BRRRR. Do you refinance and hold on to the cashout before trying to prequalify for another conventional loan or prequalify, then cashout refi? I don't know how the mortgage company is going to view my buying power or what reserves I should have to afford a 2nd rental. I suppose the other option is to refi and find a hard money lender?

I've had a lot of hard inquiries on my credit last year from trying to refi my primary residence and getting numbers run by 2 different companies multiple times because of an identity theft issue that finally got resolved this year. I'm worried about my credit score dropping again with more inquiries; although my revolving debt is now down to about 4% thanks to the cashout refi. I did however get a raise at my w-2 job so I expect everything should look good. I already have a renter lined up. Advise? Am I missing anything? 

Also, the refi on my rental is going to replace the original FHA loan; it was formerly my residence until I bought my current residence as a convential loan. Does that mean I can apply for a new FHA loan if I want to house-hack a duplex?