I am literally having the same issue right now. Its funny because you always here about the BRRR method but they never say anything about the actual refinance part of it. They actually make it sound like its no big deal. The good part is that you took action and bought the property.
But anyways, I am going through the same problem. I have a 2 family that i just did some major renovations on and I want to refinance that because there is a LOT of equity in it and I want to repay myself for the renovations. I also, just purchased a 3 family and borrowed the money from a hard money lender.
So far I have made the most progress with Pawtucket Credit Union which is a local bank. They will refinance a property under 6 months.....BUTTTT here is the problem....Due to new laws set by the credit unions you MUST own the property for at least a year to be able to take out 75% of the LTV. You CAN refinance or take a line out before 1 year BUT they will only give you 75% of the sale price.
So..if you borrowed $150k from a hard money lender for a house that was $150K and wanted to refinance or get a line on the property to pay back the hard money lender, you will only be able to get 75% of the sale price of the $150K which would be $112,000. See the problem. If you bought a house that need to be renovated you would still be out for those expenses and short on paying back the lender.
I am working on a couple other ways right now. I will keep you posted on what I am going to do.