Hey Bock, I recently purchased my first 3 deals using a personal LOC. I'm sure there are plenty of lenders who will refi if purchased through an LLC, but the lender I used said I would not have been able to refi if I purchased through an LLC.
I talked to dozens of lenders before I found newpennfinancial. Many lenders would not let me refi under the delayed financing exemption. They all wanted to base the LTV off the purchase price and not an appraised value like the FannieMae guidelines state you can do, or have me wait 6 months. But with newpenn I'll be getting almost all the LOC cash back so I can keep BRRRRing.
If the numbers work to wait 6 months that will open you up to a lot more lender, some of which should be able to refi a purchase through an LLC, maybe you might need to personally guarantee the loan.
Also keep in mind if you refi before 6-12 months you most likely wont be able to use the rental income to help with DTI.
didn't really answer your question, but I wanted to share some of my experiences. There are many good lenders here on BP, that will give you a better answer.