Are you using a hydrometer to check specific gravity of the electrolyte?
If you are loading the batteries, what was the startng voltage, and the voltage under load, and how much load?
What voltage do they indtsntly return to once the load is removed? and how much does their voltage rise in 1 hour, 6 hours and 24 hours after the load was removed?
The results of all these tests would be much more revealing as to the condition of your batteries, as what you state is occuring pretty much leaves us totally in the dark and guessing as to the possible condition of your batteries.
Regarding the new converter. 3 or 4 stage is not really relevant as to quailty, but the voltage the charging source seeks and the amount of amperage available to seek and hold that voltage is.
Trojan Specs a 14.82 absorption voltage. this does NOT mean that 14.4v will not be able to fully charge the battery, it does mean that trojan thinks the batteries will stand less chance of premature sulfating if the charging source will goto 14.82v and hold it there for however long the charging source decides to do so.
Many of us have gotten utterly disgusted with 'automatic' charging sources, those of us who actually deep cycle batteries and use a hydrometer when the automatic charging source has decided that 14.4v has been held for long enough, only to find that many more hours held at absorption voltage are required to actually top charge the battery and that days held at 13.6v or less afterwards do nothing to increase the specific gravity.
Prematurely dropping voltage on regularly deeply cycled batteries is known to prematurely sulfate them, reducing their longevity. It is very hard to stuff in that last few % and rarely will 'automatic' 3 or 4 stage chargers be able to do a true 100% recharge.
I use a meanwell powersupply capable of any voltage i choose between 13.12 and 19.23 to hold absorption voltage as long as is reuired to reah an actual confirmed sull charge, BFL13 uses an adjustable voltage Powermax converter and knows all their products and methods for achieving a true full charge.
Auomatic is certainly reassuring, but while 95% charged will likely be good enough for a few days of deep cycling, it is NOT good enough for 2 weeks of daily deep cycling and the batteries will be alking down in capacity each and every cycle, and each and every cycle where they do not get a true full recharge, will have them then require even longer durations at high absorption voltages, and perhaps a much higher equalizing charge voltage to return specific gravity to its absolute maximum.
It sounds like a converter upgrade is absolutely required in your usage, as it has allowed your batteries to get too low on water, likely with too high a float/maintenance voltage for the battery temperature, not jus tfrom you not checking the level often enough, but the single voltage charger is also not likely to ever be able to tryly fully charge them, as 13.6v for 5 days on a deeply cycled battery might not be able to compete with 4 hours of the same batteries held at 14.4v.
So If you do have to replace those Trojans and want a better automatic converter, then The PD9245 or pd9260 or PD9270, all of these have 14.8v versions and will be a serious upgrade from your existing converter, but to reach true maximum state of charge and maimum specific gravity at which maximum battery longevity is actually achieveable, you might have to override the stages and hold the batteries at a higher voltage for longer. which is simple as pressing a button for 4 more hours of absorption voltage.
If maximum longevity is not a concern then teh automatic algorithm of the PD chargers should be a huge improvement over what you already have, bt you still have the option of forcing any one of the 3 stages, and the 4th stage, while called an Equalization by PD, erronoiusly, is actually jus ta destratification charge by goosing voltage upto absorption voltage for 25 minutes every 18 hours from storage(13.20v) mode.
Trojan's recommended Equalization voltage is 16.2v. if you were to use a good turkey style hydrometer, i suspect your batteries would be in the sub 1.220 range. An extended period of 14.8v might boost tis higher, but not to the 1.280 range where a healthy new set of trojans should reside when fully charged. To get the batteries upto 16.2v for a true eq charge takes more specialized equipment and should only be done after many hours with the batteries held at 14.8v or so.
A tru EQ chrge might restore a significant portion of capacity to your batteries, or it might not, but what is impossible at this point, is even coming close to maximum specific gravity with an old single voltage converter. They stand NO chance whatso ever of getting up into teh 1.75= range at a fixed 13.8v, and there is no guarantee either that high duations of 14.8 follwed by several closely monitored hours of 16.2v will be effective either, but the latter at least stands a chance of capacity/performance improvement.
Once one acquired the tools and skills/knowledge to actually attempt to restore capacity of badly sulfated batteries, then they forever after have the ability and skills to keep their next set of batteries as happy as possible for as long as possible, if they choose to exercise them,
Many will not bother and just replace batteries sooner, and ther is no one 'Right' philosophy regarding the treatment of batteries.
I'd prefer to not treat them as disposable and simply replace when they can't meet my needs. I got sick of new batteries every two years or so, and now use 1/3 the amount of total battery capacity and am well into my 5th year of the same battery, and this is attributal to figuring out what batteries need to reach full charge, and having the equipment and mentality to achieve that, often.
And i have NO Automatic charging source. The closest would be my solar controller, but my solar wattage cannot meet the high amp recharge reqirement of my AGM battery, and this high amp recharge has been a very effective performance restorative.
While all ovr the internet there is a pronounced 'trickle' charge mentality, I think this is absolutely foolish. I say No less than 10 amps per 100Ah of capacity for flooded and no less than 20 per 100 for AGM, and if you have TPPL AGMs by Northstar and Odyssey, feed these Thirsty AGMs no less than 30 to 40 amps per 100AH of capacity when in deep cycle duty.
I regularly feed my 90Ah northstar 65 amps of plug in charging source, and my alternator can feed it upto 106 amps, my Solar on June 21 at noon at 32 north can feed 12.5 amps or so.
All my chargeing sources seek 14.7v and hold it as long as I command.
I have over 1000 deep cycles, hundreds well below 50% state of charge and am well into my 5th year on this battery. This has been my only battery since june 2015, for both house and engine startng duties. I find this most impressive and it is not just because northstar makes a top quality AGM, it is because I can high rate recharge it to a high absorption voltage, and then hold that voltage until the battery reaches full charge. If I could not achieve this this battery would have been recycled long ago.
If you can be bothered to introduce some manual into your charging source, BFL13 can link some powermax products that will allow you to hold absorption voltage for as long as is necessary to maximize specific gravity, quickly, and therefore get the best possible lifespan from your next set of batteries.
My meanwell rsp-500-15 powersupply requires some modification in order to easily, reliably, long term have voltage adjustment, and be able to output its maximum rated amperage indefinitely, so it cannot be recommended for use to those not capable of performing the modifications to the voltage adjustment potentiometer or adding ventilation or heatsinking to promote longevity of the product. I bought mine september 2014 and it has many thousands of hours on it.
If you just wat automatic, then the 3 or 4 stage Progressive dynamics converters are what I would recommend, and the 14.8v versions sold through bestconverter or PD directly are likey the best compromise of automatic for trojans. Do note that their 4th stage they call EQualization is marketing BS, and is not capable of true equalization of 16.2 volts.
Almost No converters have battery temperature compensation though, but in California at sea level this is not all that important. All manufacturer recommended charge voltages assume a battery temperature 77F. Hotter requires lower voltages, lower requires higher voltages, but I would not stress it unless 90s or sub 50's are common and one is trying for maximum possible battery longevity.