I have used a belt system similar to this for 10 years. I use it the majority of time. The brand I use is Alps. The only time I don't use it is when I'm hunting with a large group and may have to carry more than 3 birds.
Mine can hold 5 grouse or 3 pheasant. Usually, as I hunt I don't take 3 birds in the same locations, so I unload any birds when I return to my truck. On the occasion that I do shoot 3 birds I would just carry the third bird by hand back to the truck. With 3 birds the belt does get heavy in the back and tends to slip down.
Like I said, I have a couple of brands. Alps and Tangle Free. The ones I have are Danier or cloth. The next one I buy I plan to get the canvas one.
The Tangle Free belt is inexpensive; however, I wouldn't expect more than 2 years from it if you are in a lot of brush or cattails. But it would be one to try for little cost.
As for a set up, I keep extra shells in the right pouch and other stuff (ice picks, leash, compass, TP, zip ties for traps, etc) in the left pouch.