I used Loctite "Go 2 Glue" to glue suede leather over my nylon sandbag and it worked great. I put big anti-skid rubber dots on the bottom so it won't slide. I used it to glue my nylon bunny-ear bag to a homemade leather beanbag, and it worked great there too.
Essentially, it's a medium soft urethane rubber, but it doesn't spray on. It's in a plastic bottle.
You can just put dots or stripes of it on the strap, and when dry they'll grip really well.
I use Plasti-dip on my skate gloves, and it sticks well to leather and the nylon fabric too. You can spray it or dip it and I've done both. It's flexible and won't crack, but it doesn't grip like that urethane does.
I use it because I want the gloves to slide and not grip.