Added: Equalization should only be done on fully charged batteries. Your line where the manufacturer of the charger says 'on deeply discharged batteries' doesn't compute. You always fully charge batteries before equilazation or 'reconditioning' if it's the same thing.
4 hours, 3 amps & 15.8 isn't enough to do anything on wet cells. That is unless the laws have changed or reconditioning is a marketing word that really doesn't mean anything.
All my experience was equalizing on a Hart inv/charger with a link 2000 & 8, 6 volt wet cells. While cruising full time we'd equalize (recondition) every couple of months. The Link 2000 would do it's cycle pushing the voltage to 16.5 on an 8 hour cycle at almost 20 amps (bubbling quite a bit). We'd do the equalizating when in a marina. I'd shut off the electronics and start the process when we went to bed. It would finish sometime during the night. David's take on the process is the same as mine (whatever thats worth).
You need to get the voltage high enough and long enough to get all the sulfates off the plates. That just doesn't seem like enough.
Interesting part of the desulfication process is that it all falls down to the battery bottom. Manufacturers leave room under the plates for the buildup. When the batteries get old and a lot of buildup takes place the batteries will short out ( but that will take years of equalizating.