Where did you wind up?
it's been more than 1 year since the original question was posted. Where did you wind up? If you don't want to mention specific town, the county will do.
We live in Somerset county, in one of the towns that voted a Trump majority (right next to another town that also begins with a W, that went for Hillary. If' your determined you'll be able to figure it out with a few web searches). The wife and I had about a 1 month wait after submitting all the fingerprints & paperwork for the NJ FID cards (total time required was about 2.5 months start to finish).
Then for handgun permits, about 6 weeks. Local PD sends a written questionaire to the people you list as references. All in all it was not too painful. You just have to know what to expect.
I saw one post where the person went to the local PD weekly to check on status. That sounds like a sure fire way to irritate the officer in charge of handling the permits to me. . . . . . . .