Here is a running thread with NFA approval times. Work your way back for historical timeframes.
ATF continued..., SilencerTalk forum
To me, they are taking a couple weeks longer. Back in April I had a very quick turnaround on a trust
form 4.
From mailing to approval = 12 days
From mailing to pickup = 16 days
04/03 form 4 sent priority USPS; form 4 + personal check + declaration of trust
04/06 check cashed
04/16 approved
04/19 form 4 arrives at dealer
04/20 NFA item picked up
Last SBR trust form 4 took awhile.
6/08 f4 sent
6/11 check cashed
7/03 pending
7/11 approved
After it's approved, that means it's in the mail in a day or so and your class III should get it in several days then you pick it up.
From the forums they are scrutinizing trusts, so a non trust NFA transfer may actually be quicker.