BF ..... regarding what you said above: A battery charger will only stay at it's set voltage if it was designed ... and you bought a beefy enough verson of it ... such that it could hold it's set voltage at the current level that the battery wanted at that voltage.
This is what power supply voltage sag is. Voltage sag is a power supply's voltage dropping a bit when trying to supply more current than it can deliver at it's set output voltage. This is part of reason why some of our test equipment where I worked cost $300K+ per copy -> the computer controlled power supplies in the equipment were four-quadrant power supplies in that they could maintain any programmed + or - voltage at any programmed + or - current into any load up to the maximum specified current and maximum specified voltage of the power supplies.
Voltage sag is also why my RV's stock converter shows less than 13.8 volts on it's output terminals whenever my batteries are really low. :)