Well, I'm relocating this fall, too, so the only info I can provide you with is the time to process your license by endorsement.
I submit my online application and license verification (I was able to use Nursys) on 4/28. They require a "Confirmation of Nursing Employment" form to be filled out by your current employer, so I did that on 4/29 and mailed the form to the board of nursing on 4/30. My license was issued on 5/5.
If your original state of licensure and current state of licensure doesn't utilize Nursys for license verification services, there will probably be further delay as you have to submit a physical form to the board(s) of nursing to verify your license via snail mail.
I'm curious if you've had any luck, or even started, with finding employment.
My husband is a RN and is looking into the possibility to using a agency to find a job. I'll be enrolled in grad school and won't be working.