You are at their mercy. I find the time is closer to 4-6 weeks overall. Calling is pointless as it seems the call center is distant from the repair center and haven't a clue unless they link up, and give up on that idea. Just send it in and wait it out and pray is about the best you can do with DJI. Sometimes it takes two times with them to get it right - maybe. They are listed on the BBB site as A- but I'd give them an F score. Yelp! reviews are pretty poor too and seem the norm.
Good luck, but be prepared to wait.
Aside, you may be better off to send it to an independent shop too. Dronenerds is closer to you, but you'll pay for service too and forget about warranty stuff with DJI.