I DID IT! The method with the 4k60 mk2 works, but there are caveats.
My main issue was conflicting drivers. I had bought a 4k pro to test against the 4k60 pro mk2, and its driver didn't uninstall correctly. This caused an issue with how obs received the video stream from the capture card, and the fractional fps method wasn't working because of it.
1. You cannot have 2 elgato pcie capture card drivers simultaneously. Check with the software
DriverStoreExplorer.
2. Then, you must check the capture card's refresh rate. I used
TestUFO. Make sure the capture card is set as primary display.
In some cases, the refresh rate will be different whether you select it from Nvidia Control Panel or from Windows Settings.
On my system, windows 60hz measured at ~59.997hz, while nvcp 60hz measured at ~60.0017hz. Odd behavior, but it is what it is.
3. After that, go to "set up multiple displays" on NVCP, right-click on the preview of the duplicated displays and select "Clone Source: 1" (or the number your main display is)
4. At the moment I'm making this post there's a bug. Even after selecting the main monitor as primary, it still won't apply, unless you
go on Windows Settings and reset your main monitor's refresh rate. In my case 360hz -> 240hz -> 360hz, then it applies.
Now your capture card should be tearing-free and your game lag-free.
4.1. To check if your main monitor is the primary, you can use
PresentMon. Run it, play any game, then check the .csv log.
You should be seeing plenty of lines from your game.exe, running in Hardware: Independent Flip (with allowtearing = 1), and in-between them, a dwm.exe line running in Hardware: Legacy Flip (with allowtearing = 0), that's the cloned display.
If you see 1 line from the game followed by 2 lines from dwm, each with a different swapchain (e.g. 0x0 and 0x1), then neither your main display nor your capture card is the main display, this is a battle on its own.
Read more about it.
4.2. You can also check for scan line tears with slow motion camera footage, any smartphone will do. Just shake your camera in game (with vsync off), the footage should show tearing, if not, your main monitor is not the main display.
5. Now go to obs, apply the fractional fps number as you checked in step 2. I just set 600017 / 10000.
6. Next, open your capture card source properties on obs and enable buffering.
Buffering with fps mismatch between source and obs can cause unpredictable latency!
This causes audio desync, but if you set the correct fractional fps number, it doesn't. (or maybe it does, but only after recording/streaming for a long time, tbh I still have to test it out for longer than 20 minutes.)
For now, it's good enough, my recordings are in smooth motion, tear-free and with audio nicely synced.
BTW there's no need to have 4k capture utility running in the background.