This issue has been discussed at length elsewhere, e.g. on NZ Geekzone. A well-respected EVSE manufacturer in NZ has been working hard on sorting it out. BYD NZ has issued at least three OTAs in an attempt to address the issue. (Note: I have no idea what country you are writing from, nor what sort of EVSE you are using.)
I don’t own an Atto 3 but I have looked carefully into the recharging of lead-acid batteries on the Nissan Leaf, and also into the (quite muddy waters of!) sulphation of lead-acid cells.
Much much depends on the particulars of the lead-acid cell, and as you point out there’s quite a bit of difference between the manufacturer-recommended charging regimes for the various general classes of cells: gels, flooded, AGM.
There’s also quite a lot of temperature-dependence, as well as voltage-dependence and even current-dependence, on the rate of sulphation. Very roughly: at low states of charge, or in high-current draws at moderate states of charge, sulphation will occur.
Desulphation is quite controversial. Some vendors sell specialised desulphation equipment, and some advertise it as a feature on their lead-acid chargers. It’s hard to generalise safely across all types of lead-acid cells, but the cell has to be quite hot for the desulphatiion to occur at any great rate… all to say that I’m not optimistic that, on the particular lead-acid cell that was standard equipment when you purchased your Atto 3, that a charging voltage above 13.9V (but below 15V) would result in much desulphation.
A higher charging voltage (if sustained for more than a few minutes) would, I suspect, be quite hazardous if the Atto 3 charging circuitry is similar to that of the Leaf, i.e. if it doesn’t control the charging current. And, unless you figure out how to control the charging current on your Atto 3, it’ll charge a gel battery too rapidly to preserve its life-expectancy… possibly even cause it to overheat or bulge (from the hydrogen gas that’s emitted from an overly-rapid charge).
I’d guess the BYD engineers picked 13.9V as the maximum charging voltage to ensure that the lead-acid battery doesn’t ever get into the danger-zone of an overly-rapid charge. Depending on the cell and the ambient temperature, 13.9V is pretty close to fully-charged, i.e. if you want to charge it any higher, you’d have to go into what is marked in your plot as an “Acceptance Phase” (where the current is limited).
I’d further guess that some of the BYD 12V problems are with cars which are routinely left on their EVSE overnight, by owners who have used a timer-function on their EVSE to start the charge some hours after they insert the EVSE’s plug into their vehicle. Depending on how the EVSE is programmed, this may prevent the Atto 3 from going fully to sleep… and when it’s “awake” it’s the itty-bitty 12V battery powering all of its microcontrollers, quite possibly discharging the 12V battery more rapidly than the Atto 3’s normal top-up cycles (from the traction battery) will recharge it.
I’d also further guess that some of the premature fails of 12V batteries on the Atto 3 are occurring in hot climates. The charging regime for a 12V lead-acid battery really “should” be temperature-adjusted, and it might be that 13.9V is actually too high a charging voltage for an Atto 3 that’s parked up outside in the desert sun.
All to say that, if you are looking for an alternative to a BYD-recommended replacement lead-acid battery for your Atto 3, you might consider spending large on a lithium-ion 12V automotive battery. The best of breed of these have charge-controllers that are model-specific, i.e. they’ll modify the firmware in the built-in charge-controller of their units so that it’ll cope with the charging voltages and timed top-up cycles of the vehicle. See e.g. Ohmmu. Happy hunting!