There's not much of a compelling reason to deliver 60 fps content. Most streaming services will send the movie out at 30 unless you have really high bandwidth. I would suggest that you do most of your work at 30 (29.97) because that is the standard. Our brains are wired to accept the motion blur associated with the movement of images on a screen at somewhere between 24 and 30, so unless you are doing something specific that will definitely benefit from 60 fps playback and you are satisfied that most of your viewers will be watching at 30 then I would not bother producing at 60 fps.
The frame skipping, if you checked your render a frame at a time and it's OK, is coming from your player not being able to keep up with the frame rate. Standard Problem.
You should spend some time researching frame rates, video standards and use that knowledge to make decisions the that make sense in the real world.
I know I didn't solve your problem when it comes to 60fps production but you do have to ask yourself if you really need the higher frame rate.
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