You don't mention,F-Fool, if the jacket you want to carry is for warmth or rain cover. If it's rain cover, I bought a Columbia Sports Wear rain jacket several years ago that "wads up" and fits into one of it's slash pockets and then zips closed.
The whole jacket, "packed", is about 8" long X 4" wide and with a hook on the zipper pull, I hang it off my vest in the back, or toss it into the back "extra spool pocket" of my vest. But, it should store quite easily,too, hanging off your fanny pack or, even in it!? The jacket's water AND wind proof and back when I purchased it, it was $19.95.(About 4 years ago, according to "SHE, who keeps track of my fishing expenditures" informed me just now!?!).
"The shirt, with the "locker loop" at the rear of the neck", is a great idea for the net location too, if the net's not too heavy. My trout/stream net is 21"/laminated wood and hangs off a shirt loop, when not wearing my vest, with no problems.
Saint Paul-"The Highly Confused"
You cannot do a kindness too soon, for you never know how soon it will be too late.
-- Ralph Waldo Emerson