Just a thought here. The number may not be to your favor, i haven't run them, but here goes anyway.
A good private money loan might be a good option for the purchase and rehab, then refi into your conventional loan once all done.
the 203k is a great loan idea, but it's a bit of hoop jumping. you have to get bids, escrow money, pay in draws, may not be able to do work yourself, and it takes a long time to get funded (due to the bidding and valuations it needs).
I close tomorrow on a hard money loan where I'm paying 2 points up front, and 10.75% interest, with interest only payments and a 9 month term.
My "appraisal" only cost me $250, since they only wanted a BPO, and fees were less than a traditional loan at a large bank (they hide a LOT of junk fees in there). Meaning I paid about a point over a traditional, conventional loan, if that. They qualified the loan on the deal, not me. They didn't even ask for or about my credit, only that the numbers on my deal make sense. They have a 3 month minimum interest I have to pay (if I paid it off in less than 3 months). I would have closed in a week if not for July 4th giving my attorney a 5 day weekend last week.
If you could use a loan like this to acquire and rehab your place, and get yourself 10 or 20% equity, your take-out (permanent) financing would not have such high PMI costs (or none), and would also avoid some other FHA costs, so it might not cost you much more than the 203k in the end. If you recalculate your 203k loan with PMI as interest, and reverse the rate, the PMI could be costing you 1-2% in rate equivalent, for the length of the loan. They don't remove it anymore, it's permanent. I think they charge a point or 2 in up front PMI also, but I could be wrong about that. I haven't written a loan in almost a decade now.
If you don't have too much work to do, this private financing could allow you to finish the rehab work before you could even get the 203k loan funded to even start the work that way. The extra rents you collect for getting done sooner might cover the extra costs, if there are any.
Like I said, I don't know your whole scenario, and this type of financing might not be 'cheaper', but it might be 'better' for other reasons.
Worth thinking about.