Will I have room for a 83-006 on my screen doors?

I'd like to install the 83-006 on my sliding screen doors, but I'm not sure I have enough space on the door interior to do so. As you can see from my photo, I only have under an inch of flat space, or about a quarter inch more, if I were going to mount the latch/pull on the less flat area (which I'd like to avoid, but if I have to and you think that's ok, I will). I know the keeper is 7/16" deep according to the manufacturer's specs, leaving me about half an inch of flat door space, but can't find anywhere how far into the latch/pull the screw holes are (but look to be somewhere around half an inch in, which would seemingly work for me).

I need a latch that's quite secure to keep my kitties from escaping, and this one looks perfect for that, so I hope it'll work for my doors! Thanks for your help. This website and store are a wonderful resource.

I think I'll take the chance and order them... I'm sure I can fudge something a bit if needed. If the measurement was any larger, I don't think I'd chance it, but 1/2 inch should hopefully be doable, even if I have to leave the screen slid open a few millimeters (there's a lip, so the crack wouldn't actually be open to the outside).

Thanks so much for the help!