Charging RV house battery w/ EB70S

I’d like to top of my RV house batter. I have a few ideas for how to
do that. What’s best from an efficiency perspective?

120 VAC) Plug RV’s shore power feeder directly into Bluetti’s AC outlet. Let the
RV’s converter trickle charge the house battery.

12 VDC (DC5521) - Connect regulated DC output directly to battery
(with optional fuse inline if Bluetti won’t do that). This feels like
what happens during driving, with engine’s alternator connecting to
both house and engine battery.

12 VDC (Car Outlet) - Connect Bluetti’s 12V car plug to dashboard-mounted 12V car plug,
using the one that’s connected to the house battery (not the starting battery).

I’m sure I’m not the first to want this. How do you do it?

If you connect direct to the DC output in the bluetti, there is no auto shut down upon the battery being fully charged which could result in the batteries being overcharged and damaged. If you connect a small electronic battery charger to the AC, it should give good results with minimum losses but there will be losses.

Thanks, @Scott-Benson. I knew that direct connection was (significantly) less lossy than the converter (that was designed for folks using the 30 Amp feeder), but I hadn’t thought about the over-charge implications.

Thanks for suggesting a middle way.