For a simple but accurate charger just make a regulator that has an
output voltage of 2.3V for every cell in the battery (so 13.8V for a
12V
battery) and current limit the output to C/10. (So if the battery is
10A-hrs, then charge it at 1A)

I don't have a bench power supply - maybe this is the time to buy one.
I can set the voltage between 2.3 and 2.4 (they suggest 2.35) and
current limit to C/10. The better bench power supplies have current
limiters - better investment than a battery charger I should think.