1. Recorded video
2. Backing audio track
3. Recorded audio track (possibly with Audio Units applied to it)
If above three elements are synchronized in time it would be great. I am mainly concerned with audio quality, video is not that important.
First, I am guessing that you know that this will result in a video file with two audio tracks. That is great and can be played back from DVDs or files, but will not work on youtube etc.. But you probably don't want to upload there anyways, since you might run into copyright issues...
Second, I would absolutely advise you not to use your iSight camera for recording. It has a weird format (not widescreen 16:9) and performs terribly. Any smartphone or point-and-shoot stills camera will do a lot better, if you have something like that.
Third, so you are looking for a software that:
1. can apply AU plugins to an audio track
2. has good audio quality
3. automatically synchronizes tracks
4. can export video files with multiple audio tracks
Points 1 and 2 will not be a problem for almost anything you work with. AU plugins are accepted in most software, and the audio quality is great unless you mess it up on purpose.
However, points 3 and 4 will automatically set you in the range of professional software. The following three programs can kind of do what you are asking for:
* Final Cut Pro X (300$)
* Adobe Premiere Pro CC (20$ per month)
* Logic Pro X (200$)
Logic can not auto-sync the clips (as far as I know), but you might already have it or get some other use out of it, seeing as you're a musician. That's why I included it.
The first two are the most common editing programs amongst non-TV users, and they will both do great, but they are not cheap and have a steep learning curve. If you have ever used iMovie (or nothing at all), FCPX will probably be easier for you to handle, if you are very used to DAW software from your musical career, you might find Adobe Premiere more intuitive with the track-based layout. If you want more info on how to do what you want with one of these programs, let us know.
If you were looking for something less pricy, you will have more work to do. First, you will probably have to do the syncing manually. I don't know of any free or cheap software that will auto-sync the files for you. And second, you will have to export the three tracks (video, audio1, and audio2) seperately and then mux them with an external program. So it will be a few more steps, but it sure is possible.
Sorry that this is not a simple "do this" answer, but you'll have to make some decisions (monetary and conceptually) here.

Hope this helped anyways.