We arrived in DE by running as quickly as we could from NJ 2 years ago as well. Middletown / Odessa area. The inspectors want a Complete Drivers Extract.. Not the extract employers want. NJ DMV Online requires you to Crete an account, verify the account, provide extra info including your prior NJ info and your current DE info. After that it took 2 requests and about 3 weeks. Ohh it'll also cost you a bit though the wife looked after that so I'm not sure how much. IIRC under $20.
If I had to do it again I'd simply drive up and go into one of their locations and request it in person. Likely much easier. A simple call to NJ DMV for what you need, if a specific office is better and a few hours driving is the way to go. Online was a pita my wife said.
Btw.. What firearm / holster setup did you buy?
Also have you taken the course yet? We figured it would be good to take it and submit everything at once instead of taking it afterwards. I know it not required up front but I'm sure it helps streamline things with the investigators and others involved.