@Jacqui Whalley
You may be overthinking this but are on the right track. If you are using cash to buy as some have said to get better deals, that doesn't mean you have to leave it in cash as the third R in BRRRR is refinance. So if you can get the better purchase by using the cash, you do have that advantage, then find a long term refinance after the rehab and rent to return your cash to repeat the process.
My first BRRRR I financed from a local bank that held my home mortgage for purchase and rehab, up to 80% of final ARV. It was exactly what I needed as I had only 10k available. I still over-spent on it as I missed a few expenses in original budget. I survived it, learned from my mistakes, and working on my second BRRRR with the same deal.
My point is you may want to talk with small local banks or credit unions and tell them what you are trying to do and if they have any programs that could work in this area with your plans. Or if you have the cash available, just wait to refinance after and save the extra refinance fees. I didn't have that option available.
Also find a realtor with investing experience to work with in the area you are thinking of investing. Ask if they own any investment properties and/or work with other REI's. Between the 2, you should be able to proceed in a good direction with confidence as long as you have a plan on the rehab expenses(contractor, or yourself)
Best of luck. BRRRR seems to work for me. I'm sure you will get this too.