LLCs and cash out re-fis

I am a buy and hold investor who purchased and rehabbed a house that I paid cash for and am currently renting out. I have 2 questions: I recently formed an LLC. Should I put that property into my newly formed LLC? My main hesitation is that If I decide to cash out re-fi in order to have cash to purchase another property I will not be able to close/refinance under the residential side of my local lender and will have to close under the commercial side of things if I want to keep it under the LLC. I do have an umbrella policy too so I don't know how important it is to place it in my LLC. The alternative is to look for private lenders to refinance the house. I haven't explored this route yet and I am not sure to how to go about it. Any advice would be appreciated.