I will leave it to someone more knowledgeable to address the issue of removing the effect.
I’m not a pro, but I have made and sold instructional DVDs with all the video shot by me.
Maybe if you try shooting everything at 1080/60p you will get cleaner results. I have found that this creates very clean video; you can pull stills that look like they were shot with a still camera (although, obviously, at only 2mp or so).
I shoot mostly AVCHD (using a GH3) because for some reason it seems to edit better with Premiere Elements 12 (which I what I use). I output as 30p (to keep a crisp action look) but of course you could output at 25p or 24p and it should be just as good. MOV files look a lot better and cleaner when viewed on computer monitor (17″), but for me the AVCHD looks better after running through PE12.
PE12 output is very clean, both MP4 or DVD burn (I haven’t burned BluRay).
Probably the best thing to do is shoot some very short clips in various formats and see how they turn out, before launching the project.
Hope this may help somewhat.