actually, you should acquire that FCP’s native format is Apple Prores, so how about first converting it to prores 422. then, FCP must read it well and you can do some editing fluently.
Is it possible that your source file has any problem? You know all the settings u did is ok, and Prores is the native format for FCP. so it’s strange. How about trying other MP4 file?
or have you tried other software to do conversion to Apple ProRes 422?