It's a d*mned if do, d*mned if you don't so far as putting lips on those things. I bought that same WeatherTech as well as their laser cuts for the front seats specifically because of the lips. The lips do a better job of keeping snow melt, mud, liquids of any kind off the carpets or the seat backs/side fabric in the back. Personally, if I have that kind of hauling to do I use the Sienna.
If you're really worried about it, you could do something like cutting a couple of 2x2's to length, one butting up against the lip and one further into the trunk so the thing you are packing doesn't rock. Personally. I'd just keep them in the garage for when needed. If I was in the mood at some point I might paint the lumber to match the carpet.