You gotta accept that your perception and recollection of the animal will both be imperfect. Plus, there's substantial individual variety in any large mammal species. So all of your guesses are plausible. It's not out of the question you saw a mountain lion wandering New England - they can travel enormous distances alone, especially males. It's reasonable that it might have been a bocat or lynx and the angle you saw it just made the tail look longer than it actually was. It could be one of those crazy hybrid breeds of cat - 3 miles is really not that far for a stray housecat to wander.

My first guesses would either be a mountain lion with an unusual coat pattern or an escaped exotic pet / zoo animal. Besides the three species you listed, other native wild cats in the US (like jaguarundis and ocelots) seem to have a range that's much more south than New England.

can't say what you saw. eastern wild cats are clever though. especially any that are still alive under current habitat conditions.

also, housecats are significantly more survivable in low temps than we tend to assume. I have a former feral that started squatting in a friend's garage one winter during a severe winter storm (gusty wind, ice, wet) in the midwest around -5°F. he decided he likes housing and bowls of food but my friend had an overabundance of cats, so I came and got him and did the whole vet protocol.

like cats in general, he is a hedonistic baby who just wants to eat and nap and lounge cozy all day. but he is a crazy freak around winter time, bouncing off the walls to try and run outside if it's above 10°F. he sits in the window and cries at me about it. he loves snow. he likes to get in little cubbies and weird nooks in the dark, chilly basement and stare out creepily year round. if the basement door is shut, he has figured out a way to wedge it enough to bypass it. the dozen or so times he has darted out in the heavy fallen/falling snow over the years, he runs into/through piles, trills, and dances like a weiner hoping I'll chase him and "play" before eventually slithering under the steps and doing his creepy subterranean goblin routine in the frozen damp cold. he prefers to do this at night time.

he will sit there and ignore my inducements to come in, hanging out in the disgusting space under the porch for as much as 18-24 hours before a food bag shake will get him to slither out and come back in. I thought he would mellow with time, but he's at least 8 now because he's being doing this b.s. for that long. I used to worry more.

This sounds like some eerie Twin Peaks encounter

I've seen mountain lions where I'm at, and it's pretty densely populated. We see messages on the FB page at times talking about seeing mountain lions. You probably saw a mountain lion. I hear they're making a comeback.

It was an alien, you caught it on its mission to overthrow the government and it had to report back to its HQ.

I want to say Bobcat though but it sounds like a mysterious kitty.

Probably a juvenile skinny (or wet) cougar