Its a tiny loan for any institution.You'll have to get hard bids from a local GC, but maybe $110/ft?

Minimum loan amount is $250k.

Yes, you can “save” interest by paying off a loan faster - SO WHAT?  

I plan to offer owner financing to others that can't get a loan.

I do not have any loans through Flagstar Bank, but I would talk to them prior to moving it into the LLC.

I currently work with investors who are looking to begin their portfolio in turn-key real estate and manage for them on the back end so they can still enjoy their everyday lives while having a resident in place paying down their loans. 

Quote from @Jaycee Greene: Assuming you pay asking price, I'd estimate the down payment for something like that using a hard money loan (HML) would be around 40% of the purchase price and your monthly payment would be $2,600 with an interest rate in the low 7% range (probably need a 700+ credit score to get that).

In response to your original question, closing agents should handle private loans just like a bank loan. 

A combination of these things?

In addition to conventional loans and FHA loans, if either you or your wife are veterans, the VA also has a rehab program.I'd be happy to discuss my rehab experience both as an investor and as a mortgage broker, and at least help you think through your options.