Whatever. The extension cord is going to be across the street either way, so what is the difference whether it's plugged into a charger or plugged into your shore cord with a 15A/30A puck (like this, for just $2:
https://www.walmart.com/ip/Aleko-Rv15M30Fa-15A-Male-To-30A-Female-Adapter-Plug/47200149?wmlspartner=wlpa&adid=22222222228034641705&wl0=&wl1=g&wl2=m&wl3=92641189128&wl4=pla-128848208208&wl5=9031370&wl6=&wl7=&wl8=&wl9=pla&wl10=8175035&wl11=online&wl12=47200149&wl13=&veh=sem ) And your built in converter is more than likely a better charger than your simple stand alone battery charger. Probably outputs a full 45A to start, tapering down as needed as the battery SOC comes up. But do what you want; I'm just not seeing an advantage.