I don’t think you need to do any re-encoding. 1080p seldom requires that. It is usually 4K and up that needs re-encoding.
JFS tend to load all videos in 30 fps (as it did for you) regardless of the source frame rate. This is not a bad thing because 30 fps is good enough for scripting. 3 frames are 0.1 seconds and you really don’t feel if the script is out of sync less than 0.1 seconds. More than 2-3 frames can be noticeable depending on the scene I would say.