MacGuyvering an auto battery equalization? Or not?

softdown

I've got this car battery that sat for several unloved months with a "For Sale" sign pinned to its owners forlorn structure, a Ford Explorer. The battery suffered of course. The day after a 60 mile drive it only coughed up 12.2 volts at 40F. Amazingly, my decent battery tester said it is good - just needing a charge. 

I've got these Duracell 4 amp chargers that really charge a battery to 100%. While other chargers call it a day after achieving 12.7 volts, this little beast chugs until a battery shows 13 volts. That can take days on a 170 lb. battery that had showed 12.5 volts. 

This charger also has a "lithium" setting that employs higher voltage. 14.2 is what I "seemed" to measure today - at the battery terminals, not just the charger clamps. So I am trying this: After my car battery is up to ~12.8 volts I switched to "lithium" mode. I guess that will involve another day or two or three of sunlight hours charging. 

Clearly not a real equalization. But I think it might help a bit. 

Yes - I know it isn't a real equalization. I am hopeful that it will help some. 

softdown

Didn't seem to work out at all. Reset itself and showed only 12.3 volts. Though I had started the engine for diagnostics with OBD2 scanner and FORScan software. Was up to 13 yesterday - with no absorb cycle due to oncoming sunset.

Motorcraft battery made by Johnson Controls of course. Made: 3/19 with 36 month warranty. I am interested in a warranty claim - what to do? Where to go? Dealership - I would think.