Regarding the FHA collateral, I don't know what to tell you. My FHA is on an existing home, and I had to put down 3000 on a $135k home. The origination fee was a part of the 3000 down.
As for the construction, given that the housing market is less than ideal to sellers and builders, you can take advantage of it.
We are building right now. I managed to find a builder who will build for the right price, he will fund everything from start to finish. The interest of the construction loan is already tied into the final price of the bid, so no hidden surprises on that piece. The only money we had to give was ernest money. Some builders can also assist in closing costs. They won't offer more times than not but you can ask. Its not out of the ordinary to ask.