Huh, I guess the "framerate limiting" method works. Feels a bit overkill for Touhou, but if it works then w/e.
Unfortunately you've now opened a rabbit hole lol.
What you're experiencing is a specific form of stuttering called "framepacing issues". This is different from traditional "dropped frames" stuttering.
Explanation 1: Your TV outputs 60 frames per second, or one frame per 16.667ms. Your GPU outputs 60 frames per second
on average. Frames may not be delivered at the exact 16.667ms intervals that your TV expects - hence, framepacing issues.
Explanation 2: Your TV outputs 59.94 frames per second. Touhou wants to output 60 frames per second, but the GPU needs to output 59.94 frames per second. The timing is off ever so slightly, and Touhou doesn't like it - hence, framepacing issues.
Nvidia's built-in framerate limiter is decent but isn't that good at framepacing. Reset that back to off or whatever the default is.
The best framerate limiter in town is RivaTuner Statistics Server, which comes with
MSI Afterburner. Scroll down and download
version 4.2.0 Stable/Final (not 4.3.0 Beta). It's designed for AAA PC games but does work with Touhou.
Open RivaTuner. Set the "Global" framerate limit to "60". Leave RivaTuner open and try a Touhou game. Close RivaTuner when you're done.
Note that Touhou 6-9.5 may require setting up that DX8 to DX9 converter in order for RivaTuner to work, and I have no idea if it'll work with PC-98 or Seihou. Easy way to check if RivaTuner's working is to set the framerate limit to something weird, like 28.
If you want, open vpatch.ini and set GameFPS to 70; this guarantees that RivaTuner's frame limiter takes priority.
From my tests, no stuttering was visible, though Touhou's FPS counter did fluctuate a bit between 59.95 and 60.05.
RivaTuner also tends to work well with VSync On. Minimal input lag and zero tearing. This is more useful for AAA PC games than Touhou, though.
If RivaTuner can't fix the stuttering...I dunno.
Is there a proper computer monitor or a different TV that you could test?
Edit: For what it's worth, I went and looked at my Touhou 6 and Touhou 7 replays, all of them had anywhere from 0.1-0.4% slowdown, and I play on a pretty powerful laptop. All the Touhou 8 replays had 0% slowdown though.
If you don't notice any stuttering, I really don't think you should be worrying about it. IIRC one of the Touhou highscore websites accepts replays with up to 5% slowdown.
And remember: when recording and streaming, the slowdown % will be less on your current desktop than on your older laptop :p