I'm curious about the "special charger". AGM and LA have similar charge profiles, gel is different. Smart chargers are designed to make these decisions for us essentially. I've had numerous occasions where a smart charger won't sense a battery that is too low and the charger never kicks on. In this case I will jump a charged battery to the dead battery, connect the smart charger, and the charger will take over from there. Depending on circumstances I might leave the jumped battery connected for a little while kind of as a buffer for the dead battery. I've recovered a lot of "junk" batteries this way. From a service department labor cost perspective it may make more sense to throw in a battery but when it's my own stuff I'll make the extra effort.
I suggested before, deep discharges shorten battery life, over charging kills them. Deep cycle batteries are labelled as such because they have heavier plates, slower discharge rates, lower cranking amps, and can withstand deep discharges, say below 9.6 volts, and can be brought back a number of times. With cranking batteries the plates are thinner, can deliver higher cranking rates in shorter bursts and the number of times they can be "deep cycled" is significantly less before failure.
Recalling from my training, a battery with 12.4vdc is considered a 75% charge. somewhere around 12.0 or 12.2 is 50%. I'd have to go dig out my notes from way back when but I vaguely recall 11.6 or 11.8 is considered completely dead. Those values might be enough to get some dimly lit interior lights or dash lights but not enough to deliver the 150 to 300 hundred amps required to crank.
At any rate, if OEM says use this battery and that charger then best bet is stick with recommendations.