Hi,
In my opinion you would be better off sticking with the long term financing you have on this one already.
The BRRR method works best when you purchase a property (usually distressed) for a significant discount. I have been using this method quite a bit. When I buy I make sure I can purchase & rehab for less than 75% of the ARV. It's not easy to do but when it happens, I can refinance as soon as the renovations are complete and cash out everything I put into it. Here's an example of a SFR I just refinanced last week:
Purchase = $74k
Renovations =$40k
ARV = $195k
Cash out refi loan = $146,250 (75%of ARV)
After taxes and holding costs I was able to pocket about $20k from the refi and the property cash flows about $300/m after reserving for cap ex, & vacancy.
These aren't easy to find, but they are definitely out there. I unsuccessfully tried to buy this one off the MLS last year but kept an eye on it and jumped on it when it went to auction.