FHA inspectors have to follow guidelines and everything MUST be up to code, or else it is going to be written up on their report. Also you mentioned that YOU, or some of your family members may do some of the work. That will NOT be allowed.
When you do a 203K loan, all contractors must be licensed and insured. You CANNOT do the work yourself, it will not be allowed. What you do have control over, is which Licensed contractor CAN do the work. Just because you received an estimate from one contractor, doesn't mean you MUST use them. I am dealing with a 203K loan now and the buyers have a friend that is a Licensed Builder & Contractor and they are more comfortable with him doing the work than a total stranger.
So this contractor must submit his estimate on his company letterhead, and the lender uses that as part of the "file" or approval process.
The great thing about a 203K loan is you can add things to the loan that may never have crossed your mind, such as granite counter tops, etc. Your lender can guide you in this process because it can get a bit confusing, and time is of the essence, and it sounds like you don't have a lot of time to waste.
I hope this helps and feel free to email me with any more questions.