I finished attaching the driver's mat to the carpet (so it won't slide around, an obvious potential issue). It took about an hour to remove the clips, make some modifications to the mat and carpet, and reattach everything. It's now extremely snug and stays put just like the factory intended. This required relocating both clips on the driver's mat.
I relocated the clip closest to the door by making a new hole in the mat itself and relocating the female clip as well as moving the male clip on the carpet. The female clip in the mat is a bit tricky, but with a tiny flathead screwdriver I could disengage the retaining clips and split the two halves. The male clip is a little easier, as it only has one tang that needs to be defeated to open the butterfly clip and remove it from the carpet. Clearly, a picture is worth a thousand words here!
Once that was complete, you can see in the photos where I made a new small, round hole to install the female clip into. I used a sharp knife and just cut it free hand (CAREFUL!). I then inserted the male clip in this newly located female clip, put the mat in place, and used this to mark the carpet where new slots needed to be installed. I cut two small slits in the carpet with a sharp knife (CAREFUL!), same size as GM did originally, then slide the male clip in and snapped it in place.
On the clip that is closest to the shifter, I did not modify the female clip and only moved the male clip. Just as with the other male clip, disengage the retention tang, open the butterfly, and remove it from the carpet. Put it in the female clip, mark where the carpet needs new slits, use a sharp knife (CAREFUL!) to cut two new slits, install the male clip and snap it all together. I forgot to take an "installed" picture, I'll try to get one soon. It looks just like it should, of course.
Click! Click! Snaps together nicely.
Such a satisfying feeling doing a simple project like this and making things work nicely.