Regarding a 5 amp/ 5% charging source, Some of us have employed adjustable voltage power supplies like megawatt, Meanwell and some of their Chinese clones.
I have a ammeter online on my output and can, if I choose to sit there and monitor it, twist the voltage knob to maintain a solid 5% of the 20AH capacity flowing into the battery until desired end voltage is reached.
I once pushed a 22.59$ clone past its limits for science, but it easily could have done this 5% thing all the way upto 15.33 volts.
It smoked as it was a 350 watt power supply producing 532 watts for 17 minutes till the smoke escaped as it had no current overload protection.
Do a search for Cheapowatt or Etopxizu for a low dollar solution. I don't know if it is a lower dollar solution than a 50 watt 12v bulb though.
