Consider to mix your video in a proper multitrack video editor. Record your music to an audio workstation. Record it also to the video as you shoot your performance, but only to be used as a sync guide. Use in the rendered video soundtrack only what's mixed well together in the audio workstation.
It has been possible at least 10 years to import to a video editor a mixed music track and get it synced to the video which was shot by listening the same music track. The devices stay in sync so well for ex. 5 minutes or even more without any special syncing hardware. What's captured to the video can be low quality with no harm, if the stuff captured to the audio workstation is good.
Do not expect you can easily make plausible looking instrumental solos or vocal performances on the video by trying only to play or sing in sync with a prerecorded performance and by using only the prerecording as the video soundtrack. Extremely well trained persons can do it plausibly. 2...3 second quick clip may be successful easily, but not a longer passage. All long important solo parts must be performed and recorded to the audio workstation at the same time as the video is shot if the performance must look good.
If there's something so tricky that occasional errors must be fixed by re-recording you may meet a moment where the video and audio do not fit well enough. That can be covered by showing in the video something else.
ADD after reading again all given comments and other answers: The method above is nothing big nor complex. It only uses common tools available for everyone and gives a possibility to get something more finished than the linked video but without increasing the complexity substantially. BTW the video has quite good sound, but the skills of the performer are worth a finer production.