Well we live in a market that supplies most every combination of everything. The era of the single Telecaster model fades into the black&white past.
I'm as guilty as the next person in liking electric guitars as statuary, loving the colors and shapes, and I have a long, fond relationship with Telecasters. So if you want everything you want, colors, shape, pickups, trem type, etc. you can look around for it or build or commission a custom model, and it's your right to not compromise on any of your specifications.
So having said all that, it's always possible that what you think you want and the results you actually want are not the same. This isn't a knock on you or your request. It's just a universal possibly in these things, for you, me, and the next person.
Trem systems differ, sure. The Strat style bridge and it's decedents like the Wilkenson, are the most common. You likely have used them, and have some idea of their particularities. if only because of that. I've grown to like Bigbys, and since it design and designer are from the same culture that gave us the Telecaster there's some artistic consonance in using one on a Tele. The Jaguar/Jazzmaster trem design is very smooth, and once you deal with the bridge issue it's really a great system.
Here are a few "not what you think you want, but..." things to consider.
Someone's mentioned the Jaguar or the Jazzmaster. Despite the short scale, the Jaguar pickups do a pretty good bridge Tele sound, more so that most Strats. Jazzmaster pickups get something akin to the Gretsch sound. The current Squier J Mascis model is a great guitar right off the rack in my experience (and it has a TOM bridge so no finicky setup needed).
If you want the sound of Gretsch pickups, but are hesitant to do your own mods, you really should consider a Gretsch. Are you sure about Bigsby's? The current Electromatic line seems good.
It's a mod, but besides Bigsbys, there's the Stetsbar add-on trem system. I've never used one, but I used to work with a guy who said his worked well.
https://stetsbar.com/
Or course if you really want something different in the shoe gaze genre, there's always the Tele with a B-Bender. There's a sound that's just waiting to be exploited in that context!
Again, not meaning to deny you your dream guitar, just mentioning options.