You found the correct way to use 1/60 as fps, and it's correct OBS becomes slow and clumsy.
You seem to want to create a timelapse video. In a timelapse video, not only the source fps is important, it's also the fps of the intended timelapse. If you just tell OBS to record at 1/60 fps, any media player will show every frame for 1 minute, then go to the next frame. So you need to speed the video up with some postprocessing software - OBS itself isn't able to do that.
I assume you want to speed up time either by a factor of 3600, because you might want the final timelapse video be 60 fps, so from 1/60 fps (raw source) to 60 fps (final) is a factor of 3600. Or you wanted a speedup of 60 and didn't think of the fps of the final video.
If you want a speedup factor of 3600, this is an appropriate ffmpeg command line to create such a timelapse video:
ffmpeg -i input.mkv -filter:v "setpts=PTS/3600" -an -r 60 -c:v libx264 -preset slow -crf 10 timelapse.mp4
The term "PTS/3600" does the speedup of the source by a factor of 3600, and the parameter -r 60 will create a 60 fps video, so it will look really smooth. You will see one hour (3600 seconds) of recording will become a 1 second timelapse video.
If you wanted to speedup by a factor of 60, thus 1 hour recording will get 1 minute timelapse video, this is the ffmpeg command line:
ffmpeg -i input.mkv -filter:v "setpts=PTS/60" -an -r 60 -c:v libx264 -preset slow -crf 10 timelapse.mp4
Interestingly, the fps of the original file recorded by OBS doesn't matter. You just have to make sure it will not contain less frames than the resulting timelapse video.
For speedup 3600, the fps can be 1/60, but as you found out this will make OBS very clumsy.
For speedup 60, you need 60 times the frames, so you should record with no less than 1 fps within OBS.
And this is the fps I recommend for your recording, even if you plan to speed up by 3600. With 1 fps, or perhaps even 2 fps, OBS is responsive enough. And the above ffmpeg commands just throw away the not needed frames. With 1 or 2 fps, the file size of the OBS recording should be still small enough even for day long recordings. And you are free to experiment with the speedup factor if you find 3600 is too aggressive.
Make sure you use *.mkv as recording format within OBS, because this format is robust against failures and crashes. If you use *.mp4 for the raw file, and your PC or OBS crashes, the file is broken and cannot be recovered. *.mp4 needs finalization at recording stop, so every *.mp4 has to be stopped gracefully, which might not the case if a recording runs for days.
