Regarding the charger, I have a used 60W 12V power supply which can be adjusted to 13.5V. It is a pretty decent car battery charger. But I suppose something like 300W - 600W would be more useful for you.
(Something like this
. Note the trim potentiometer on the right side of the connectors.)
The boost converter is a good idea! Just get a powerful enough one … I had to put on in silicone oil to keep it from overheating when powering my laptop.
If you get one with adjustable voltage and current, it doubles as LED driver for high power LEDs.