Do the NVidia drivers have a frame rate limiter feature? (sorry I'm on AMD and its been a while since I had NVidia)
With the AMD drivers there's a frame rate limiter (Framerate Target Control) that you can just set at say 144 (or 145 to be safe) and it will target that as the max. Check if NVidia has that ...
But ... if you cap your FPS at 144 in
any method, you'll NOT benefit from the extra 56 FPS in input lag reduction you might get from playing at 200.
So in that respect, VSync also shouldn't be causing much input lag beyond the 144fps either, as long as its locking to 144, and not to like 120 or 60 or something. It causes "input lag" because it is essentially lowering your potential FPS to a much lower one that your monitor can handle - but at 144, as long as that is your FPS with vsync on (and not lower), would still allow "144FPS" input response ... but not 200.
GSync, will match the monitors refresh to the GPU (as far as it can) to get rid of tearing, but unless you can "overclock" your monitor 144 is the max you'll get out of that as well.
The question becomes "Can I get rid of tearing while still greatly exceeding the hz of my display?" -- the answer, as far as I know, is no.
So you either turn off all the fps smoothing features and put up with tearing, or you live with the ever so slight input lag of going from say 200FPS as you mentioned, to 144 FPS to match to your monitor ... I doubt there's even a noticeable difference, but I'm not that type of gamer ... (I prefer things looking nice

)
Disclaimer, I'm not one of those gamers who buys a $1200 2080ti, and plays with low quality and 720p monitor so I can get ten billion FPS in hopes I can "win" a game, so I have only knowledge and logic on the topic and not experience in the direct area of your question.
On a side topic ...
If you have a
freesync monitor, is turning on gsync even a good idea? It doesn't seem like its working anyway ...