Easy, make sure the media bin only holds media that has been used (to remove unused media first, "Tools-Clean Project Media". Then "Save As" and select "Copy media with project".
Yes, VMS backsup the whole original clip, trimmed parts are only saved when the antique DV codec is used. Setting those handles doesn't work for other codecs.
To program it is very easy, as most of it is already there. It's only in the decision how to re-encode and this can be set by the user as any render template.
If it's not in VP also than it's a weak point in an "alleged professional" NLE.
From all the NLE's I know and have experience with (VMS, Vpro, PD) there is no one who saves trimmed versions of used media. They always save the whole original media to avoid re-encoding and quality degradation, even PD, who's able to save a lot of video formats without re-encoding.
The only solution I know, but not familiar with, for Vpro is to use Vegasaur for trimming and rendering without re-encoding parts of the timeline. When you use these trimmed renders as media for your project, than you can backup those with your project.
Yesterday I was in a Premier Pro webinar (part of "Post|Production World Online") and there this feature was shown. Just as expected, with handles setting and transcode templates.