Softener GreenSand GAC

I have a water system set up like this. Chlorine injection to retention tank followed by Greensand filter followed by GAC followed by softener. The Iron level is low, 0.022 but I had the Greensand from the old well. Hardness is 690 Mg/l or 40 grains. My question is what would be the proper sequence for this system? There is some rotten egg smell the water test shows Sulfate 93.0 Mg/l. The greensand regenerates with potassium permanganate every 4 days since I have the chlorinated water going in (continues regeneration). I was thinking to take out the greensand filter since iron level is low and just use the chlorination followed by GAC then softener. A water company told me that I should soften the water first then inject chlorine followed by GAC.
I was also thinking to switch the chlorination to a H2O2 peroxide system. Any thought on that? Is it expensive to run? We are 5 people in the family and I would say 500 gallon of water a day.