I spent 20+ years in NJ.
I have now spent 20+ years in GA. I have family in Alpharetta, including 2 of my grown kids.
You have no idea how much your quality of life will improve.
And I think the cost of living differences are much bigger than 35%. My mother relocated 8 years ago. She was on a fixed income in NJ of about $60K living alone, going $2K negative every month. I was supporting my family of 7 for less than that. (Rural GA, not Alpharetta). She came here and made essentially no life changes, but now gives away nearly $2K per month.
You won't see that big a shift near ATL, but it is MUCH bigger than you realize.
You have the highest taxes in the nation. Oil bills, home heating costs, winter clothes, snow tires, salt deterioration on your cars, the list just keeps going.
You will still have traffic in ATL, but you are used to that. And ATL is addressing it with infrastructure development, NJ is just surviving it. You would make that transition better than I would.
Play hardball, but consider it seriously.
You have said you could work remotely. What about keeping the current job part time for an interim, while trying the new one?
Atlanta is a huge market, and your skills are easily sellable. I see no issues with employment security.
Regarding the dogs: they will be MUCH easier to accommodate in GA. There is still some open space.
Definitely do not buy anything before living there. Within a fairly short radius from Alpharetta there is a huge variation in geography, culture, community, etc. You won't know until you live there.
Regarding your wife: you have a bigger problem. You haven't mentioned FL, but I think the two of your are on very different wavelengths regarding your long range plan.
Good luck! I am excited for you!