I'm not very knowledgeable on the subject, but will be subscribing to ths thread because I plan on doing something simular.
I do know that wait times are averaging 6-10 months (closer to 10 is what I've heard lately).
I don't think you will be allowed to do anything regarding NFA to your gun until you have your tax stamp in hand and everything is finalized.
There is no guarantee you will be approved, but unless you have a shady past, you should be approved.
Is there a chance that the paperwork will be lost? When your dealing with the feds, there is ALWAYS a chance they will screw something up.