Is that you in the photo? That's King of 2 Mile, at the Whittington Center, world famous if you follow long range shooting. 1200, they don't shoot during that, but it's badass for other things as well.
CT is pretty far from NM, and I searched a ton on CT, both in gun laws in the past, and recently, on ranges there. You have to be shooting on private land, for 1200. There's no other way around that. Private land isn't "classified" - but you can use any words you want. Furthest range I found in CT was 200 yards. I searched alot. Most pertinent, accurate results:
https://ctguns.org/t/list-of-connecticut-shooting-ranges-and-clubs/580
If you have a friend with a 1200 yard range, in CT, he could easily be a millionaire. There's nothing close to 1200 yards in New England, unless you venture to Quantico. I lived in Northern VA for a couple years, and as retired military, had access to the Quantico range, but only to 1000 yards. The wait list for non-military was years long, for civilian shooters that were trying to buy a membership. Regular Members and Associate Members were a vastly different category -basically, if you weren't Active Duty, or a Retiree with 20+ years, you weren't getting a Regular membership. If you were "veteran" meaning you did 4 years or whatever - not a career with 20 - you were competing for the Associate Membership - and that was a TIGHT process, years long waiting list...
You might look into it. Everything is New England is close. It's not even like driving across Texas. Easily doable for a good day of shooting.
https://quanticoshootingclub.com/membership
Then again, you have access to a 1200 yard range in CT. That isn't public. Has to be private, nobody in CT has heard of such a thing - which is why I asked about pics, next time you're there. It's interesting, to say the least, and unheard of for that area...