Cool, I'll try the big gun and let you know how it works.
I tried the hair dryer on the leather as I was gluing, I dunno how much it helped. I wasn't sure about how long to heat it so I used a hair dryer instead of the heat gun.
And yeah, it's contact cement that I got, I scuff-sanded the foam and sprayed both parts when gluing. I won't tell you how badly it was sprayed out of that touch-up gun, though.