My dog also goes in and lies down quietly. He considers my tent his crate! I pull pad and sleeping bag out of the way when we go in at night and before we go out in the morning.
It also helps a lot to keep the dog's claws clipped short. I try to clip my dog's claws twice a month. Frequent clipping makes the quick recede so that you can cut them a little shorter each time. I have always, since he was a pup, given him a dog biscuit to chew on while I'm doing the pedicure on each paw, so he's really good about this procedure.
I don't use the NeoAir; I have a KookaBay custom pad instead. Protection is needed, though, whatever air pad you use! Before pitching my tent, I check the site carefully to remove anything that might puncture either the floor or the pad. A piece of 1/8" Gossamer Gear Thinlite pad (cut to a little longer than torso length) under my air pad also helps--protects the air pad, cuts down on slipping, adds a little extra insulation for really cold nights.