You are confused about charging profiles between battery Bulk and Absorption and converter voltage "stages" of Boost and Normal.
A single "stage" voltage above battery voltage will take the battery through two profile stages Bulk then Absorption. You saw that with your 13.6. With three-stage converters, the Boost stage can also take the battery through Bulk and into Absorption while still at that single Boost voltage.
Ideally, the charger will do constant amps while taking the battery all the way to its Absorption, but unfortunately PD converters don't seem to do that.
They let the amps slide somewhat instead of staying constant. However, the amps stay up enough so that when the battery starts Absorption, the amps start to drop quickly and you can see the "knee" when that happens. (Other brands of converters and chargers do the constant amps properly, but some may not have a control like the CW. You have to pick and choose what features you need and don't need when shopping)
Your PD is working the way it is designed to. Note in the manual how long it stays at 14.4 when triggered by the CW vs how long just doing Boost by itself.
Your batteries are in bad shape, as indicated by your hydrometer readings. The PD cannot fix that, having only 14.4v. You need some time at 16v to desulfate them, if it even can be done when they are that bad.
You have a good enough converter now, so the next step is to get decent batteries.
