The beefed up screened door seems to be doing the trick - keeping the cats safe and secure. However, a unforeseen consequence has come to my attention.
Now, I realize most people would probably see this consequence as a positive thing. The screen door now closes tight against the frame which leaves less of a gap around the door for moths to get in. Less bugs are getting in and that is putting a damper on the nightly moth hunt.
My mind is already at work trying to think of some possible solutions. I may replace the screen on the side windows with the wire mesh material I used on the bottom of the screen door. It has larger openings which should allow more moths to enter and would be stronger than the existing screen which would be helpful in keeping any crazy leaping cats (Theo!) contained.