Moving with a C&R

I think a Mosin is the first requirement, lol! Sorry I can't help on how long it takes to get the address change done, I haven't moved since I got mine.

I just changed recently, and it was about a month, maybe a bit less. Roughly the same time it takes to get it in the first place.

Mosins are highly recommended, for both price and fun factor. Remington 513T because everybody need a military trainer. M1 Garand because it's mandatory. CZ-82, great value. Springfields, Mausers, Enfields, etc., find what rings your bell and go nuts.
RT

M-1 Carbines are a must! Of course, you can buy 5 Mosins (or more) for the cost of one carbine, but that's not important right now.

It took a month, maybe close to two months if you count requesting the forms and mailing time, when I moved.

Just search "C&R" or "C&R dealers" on here and you should find several threads with links to businesses that have all sorts of stuff you've ever dreamed about putting in your safe. But here's two to start with:
classicarms.us
allans-armory.com

Also make sure you check out the CMP's website.

A month is about right...depending on the time of year.

Another recommendation for a Mosin.

I recommend getting a K31 swiss, Jgsales.com is running a sale. Classicarms.us also has some, as well as ammo

Best shooting milsurp I ever got

It took 3 weeks to get the new license. No issues that I recall.

ATF requires notification from a licensee (that includes you now) 30 days before a move. If you are moving next week, I would call the FFLC tomorrow (866-662-2750) and ask them what to do.