I am a big fan of those PowerMax LK converters (bestconverter rebrands his as in the OP) for their flexibility in choosing either automatic three stage or else choosing single stage adjustable so you can meet any battery spec but do it manually at the times required for your own scenario.
The problem with the OP lower portion type is after you install it, howinheck can you get at the setting controls???? The deck mount kind is easy. Just tuck it in under there with the side that has the two setting holes to the front so you can get at them.
On "four stage" vs "three stage" that is from some converters calling their fourth stage which comes on every so often (varies by brand how often) "equalization" when it is not. "Equalization" is an overcharge after the battery is full using say 16v to do a proper desulfation.
The "fourth stage" boost every so often to the 14.x "boost" voltage while it is in "storage" of 13.2v (third stage), is actually just to stir the electrolyte and should be called "de-stratification"
Anyway, you can get a deck mount 60 amper in there and find a way to get 120v to it from what's there now. Some cut off the converter's plug and wire the cord to the OEM 120v. Or use a nearby 120v receptacle, whatever.
Check out boat and Rv which usually has lower prices than best converter for those PowerMax converters, but not always in stock. He has lots now:
https://www.boatandrvaccessories.com/collections/rv-camper-fifth-wheels-battery-converter-chargers/products/powermax-pm3-60lk-12-volts-60-amp-power-converter-battery-charger-w-led-light