Okay,
Ive been through ffl change of addresses and changing ffl types, one as recently as 9 months ago.
For my own shop, changing addresses I got my new updated FFL with new address from ATF inside of 3 weeks. This may be the exception and not the norm but thats what it took last July.
Even if you do not have an updated FFL with current address, you can still log firearms into and out of your FFL bound book. Since you already owned the barreled action, it should have no bearing on his being able to log it back out to you.
On my manual machines I can chamber 2-3 barrels a day if things go smooth. I can build a rifle in week including cerakote, pillar bedding, hydrodipping, chamber and muzzle brake work. But if you come to me for a rifle I'll still tell you it'll be 6 months before you'll see it. Getting barrels and stocks is becoming quite the hassle. I've had rifle projects that have lasted well over a year for one reason or another and I'm making plans to shorten the lead times as best I can. The last year I've averaged a 6 month turnaround time for a carbon barreled build using one of my own barrels. Sometimes they take longer, sometimes less.
When a customer brings me an action/barrel/stock and has me build it for them, I quote them 4-6 weeks and haven't been late on one yet.
Mike