I have used everything from vests, to Fishpond chestpacks and for the last year have used the Orvis sling pack. The situation was similiar to yours, I ended up attaching a carabiner to a place on shoulder strap, with long 2ft or better bungee cord (available everywhere). I throw the net over my left shoulder, and when I need the net I just follow the black cord up the shoulder strap with my hand (after a while you won't even look) and flip around or over my shouler. If you can find a place for the carabiner should work on your bag too. I am convert to sling packs now and will not go back after a year of heavy use in all kinds of water.
(As a side note, if no place to attach on shoulder strap, just get a piece of webbing, make a loop, insert a D ring in loop and have someone sew onto shoulder strap with heavy thread (a seamstress or dry cleaners probably could do that for a small charge.)