Does the material get harder? I wouldn't claim that. It does stick better the longer you let it sit before use. And I know that's hard. None of us really want to let our toys sit unused lol. So far it looks like the film is doing its job. I would assume that the front edge where it is lifting would hold up a little better under two conditions.... maybe three.
1- let it cure longer
2- if you have access to a leaf blower, clear the parking lot of stones.
3- if you think your getting to much scuffing after you cleared the parking lot of stones... Raise the ride height some.
This stuff isn't indestructible. Stones will tear it up. In my mind it is more of a scuff protector for when you car bottoms out on occasion. Not a stone proof shield. The harder you are on it, the quicker it will wear out and need to be replaced. This may not work as well as you were hoping but I can say that I don't think a similar product from another source would work any better.
Oh and to get the film off the paper backing with out having to cut it, pick an edge, make a clean straight cut from there to the outside edge of the film sheet. Then you should be able to start pealing from that clean cut to the edge of the outer chassis score in the film. Slowly pull along the score line in the film and you should have no problems removing the excess material along the chassis protector. Atleast, that's how I did it and I had no stretching. Here is how clean it came out for me. You can barely even tell it is on there.