As alluded to before, FHA has their appraisal and it is what you see the home listed at, so if your lender accepts it, that part is done. Consult with your lender as to their appraisal procedures, I've had them go both ways.
Inspections can be done in a day, so that is not going to be your slowest part of the system. In my experience, it has been title that slows us down the most consistent, usually because of demands. Demands are the debts that remain on the property to put it simple (trash, sewer, hoa, sid/lid etc.). The more demands you have the more difficult it seems for them to close on time, you also do not get to choose title so there is no way around it.