This sounds like a loosing propsition.And you should call the lender about borrowing the 30% and living in it... if you lie to them and then they find out you will be in a worse situation than if they say no now.

In Georgia we have to bring cash or equivalents to the auction so you need to have the cash, a backer or an asset to borrow against.Its a high risk/medium reward proposition in my area, but your results may vary so make sure you understand that going in.

Borrower typically pays all fees including appraisal fee, title fees, attorney fees for docs, insurance, etc.

I am not afraid to borrow money on a variable rate at prime + X%.

Has to be cash for it to work properly. if the cash is borrowed, BRRRR just does not work well because you just pay off one lender with another. the amortization should be the amortization of the loan you expect on the refinance stage. 30, 25, 15 etc. depending on your loan you expect to receive to get cash back out. 

Correct, if you want to procure a conventional, agency loan (IE, Fannie/Freddie) at the lowest rates/fees, you'll need to quit claim deed the property from the LLC to the individual borrower(s) name(s). 

I don't want to get locked into borrowing money for 30 years at a 7-8% interest rate which also charges a penalty if it's paid back early.

However, if you are using borrowed funds as the down payment (ie HELOC), do you plug that in as "cash" even though it's debt?

Example would be if you borrow 100% of the purchase and rehab let say $150,000. 

I borrowed $100K to save them after the 2008 Crash and stopped payment for a year.