How to replace the audio in a video on Logic Pro 11?

Hi folks,
I often record videos of my live performances, but since they’re usually captured with my phone’s built-in microphone, I always have to record audio externally and sync it later while muting the video’s original audio. I used to do this in Reaper, but even after installing VLC for encoding to preserve the original video quality, I still don’t get the same video quality when rendering in Reaper. The audio is fine, but how it looks isn't satisfying as far as I understand, having asked for sighted people's opinions. I also tried installing FFmpeg, but that never worked with Reaper either.

My question is: with Logic Pro 11 trial, how can I do the same and export the video while keeping its original quality? Is it possible with VoiceOver? I don’t know much about using Logic Pro, but I’ve got a bunch of projects I need to finish, and I don’t really have time to learn it from scratch right now.

Here are the steps I want to perform:
1 Import the original video.
2 Import the recorded high-quality audio.
3 Sync the professional audio by scrubbing and matching it to the video’s original audio.
4 Mute the video’s original audio while keeping the visuals.
5 Export it in the original quality/format/size.

Thank you!