I went thru the BATF/Class III process with a SBR I built last year and it's not that difficult, just time consuming. The main things to worry about are making sure all the T's are crossed & I's dotted, all forms are completed plus you don't assemble the gun until AFTER you have received the stamp.
There's a lot of discussion about having parts for a class III project in the same location before approval from the BATF arrives in the mail. I talked to three different ATF agents during the process and essentially, as long as you don't have the parts kept together - in the same gun safe or work area - and can't be readily assembled, they have no problems. Also, if you have other weapons the SBR parts can legally be used on, the feds have no problems with them being in your possession.
Realistically and all paranoia aside, no ATF agent is going to come to your house and check on your SBR project unless, possibly, you are on a federal watch list or you're an FFL holder/dealer and the ATF already has the right to visit anyway. I know of no private citizen (I don't count third hand, read it on some internet forum, horror stories) or know of anyone who knows of anyone that has submitted class III paperwork who's had a visit by the BATF concerning their build if the gun is kept at home or in the local dealers shop. The few cases I have heard and read of involving the BATF and class III weapons is when someone assembles or buys one and is caught in public. Usually, someone sees you with the weapon (FYI 95% of the reports involve full auto guns or pistols with suppressors) then reports it to the police. The local LEO's could pay you a visit and/or report it to the BATF and they pay you a visit. If you carry a copy of the approved form 1 & stamp with you when you have the gun in public, you eliminate the questions about whether your class III project is legal.
OTOH, if you want to play it safe but still don't want to wait six months before starting your assembly process, buy the parts to build your SBR and have a friend, relative or local gun shop keep them for you until the stamp arrives.