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Meal, from what you described for the behavior of your battery and from what I noticed on similar batteries , if a battery can keep a V reading for above 12.6 but quickly drops when loaded, this is an internal short or high internal resistance, if the internal resistance is at the internal connections, this in my opinion will not make you feel the battery is getting hot while you are charging it or while you are discharging it because the internal connections part that will cause the problem (the pivot) should be above the electrolyte level, you may feel the warmth with an infrared temperature sensor directed at the top of these connections but the battery will not heat up.
In the case of your battery, and as long as you did not find much impurities in the electrolyte when you drained it, then I would eliminate the possibility of consumed plates, when the plates are consumed, particles of the lead will settle down in the battery and the electrolyte will be dark in color, when you filter it, dark impurities (lead) will show in your filler.
I have no experience with calcium based batteries so I cant help in this area, but my understanding is that if it is mechanically sound, then why not treat it the same way as desulfating normal batteries? may be a higher or lower current is needed but the concept should be the same.
Traction/ deep cycle batteries has thicker plates as you know, so chances and time needed to consume (cause a hole) in the plates takes more sever circumstances and time, that is why their repair rate should be higher than other batteries.
Tetrasodium / EDITA did not work with me, I'm contacting some people who claim they have better chemicals that removes sulfate, I hope they are not cheaters, if I buy any of them and they turn out to be true, I will tell you.
You say your pulsars are dangerous to the uninitiated, isnt that the case with all our desulfators?
the difference will be that your's give assured results.