I have never dealt with that much Hydrogen Sulfide so I won't pretend to be an expert. 6- 10 is about what I'm used to and we get rid of that with an air pump and a galvanized tank. Nothing more.
I for one don't like injecting chlorine especially if it's not necessary. And even more so with a Stenner. If your Stenner comes on slowly, it may be that the flow switch is gumming up with sulphur or it may not be hooked to a flow switch. It may be coming on with the water pump.
Aeration, Chlorination and Carbon filters are three different ways of dealing with sulphur odor. Why all three I'm not quite sure. Maybe it's what is needed to get rid of that much sulphur. The carbon filter will deal with about 1/2 part per million and that's about all. Chlorine will treat much more as will aeration, but how much I'm just not sure.
My system works very well on all the water we have treated, but again, that's not much over 10 ppm.