The # 1 reason batteries die is due to sulfation buildup on the battery plates. Some of the newer battery chargers/maintainers are designed to "shake" the plates so that the sulphur is broken up and mixed back in with the battery acid. It seems that you may have a dead cell and nothing will help that. I also have had the "green eye" showing a charge but developed a bad cell and a battery that would not hold a full charge.
'01 2500hd ext. cab, 8.1 litre gas, 5 sp. Allison auto
3.73 rear end
Mag-Hytec rear diff cover
Amsoil Dual by-pass oil filtration system
Amsoil synthetics all around
265 watt AM Solar, Inc. system