I purchased my first restricted firearms on March 29th; two pistols and an AR. Got a call from the store this afternoon (April 7th) that the approval came through. I had called the 1-800 # on Tuesday, April 5th to get an update and was told that the application was pending. The agent on the phone also suggested that I fax in a copy of my range membership and put my transfer reference # in the RE: line of the fax. They went on to clarify that although this was not required, it may help speed up the process and the information will be stored on my file. I sent the fax on the same day. Not sure if it made any difference but thought I'd share my experience.
I am told that the first time one buys restricted firearms the process takes longer than normal, in my case it took 7 working days.
Cheers!