Well, we have 17 nights under our belts camping with Kansas and a couple of breaks in the screen on the screen door to show for it. So in looking for a solution I found that they make a pet-specific replacement screening that is available at the big box stores. So I replaced the bottom portion with it. It does seem very sturdy and gets good reviews. It is some sort of plastic rather than fiberglass. So time will tell if it holds up to someone scratching at the door. Side note: he was so cute napping in his bottom bunk the majority of the time we worked on mods this weekend!
The other things I did were to put springs on the screen door to make it close automatically (I had done it before, but let's just say I didn't read the directions and installed it all wrong.) So this time was a success, and since I had to remove the gas strut door opener to get to the hinge screws we decided that we liked the ability to open the door all the way rather than the 90 degree angle that the strut allowed. It is easy to put back on, so we'll keep it in the camper in case we change our minds.