Battery charging

I've a converter that will charge at up to 60 amps, an inverter that will charge up to 90 amps (and blow the in-line battery fuse!), and a solar controller that will charge at up to 40 amps. Battery bank is four T-105s. Although I usually leave the converter off, the other two are left on. There's no conflict between them and they don't overcharge the batteries. Once charged up there's only about 1 amp positive indicated on the Trimetric monitor and they do this all themselves.

12 amp IS a trickle into 4x GC2. No worries about on-board equipment. Just slap it on and charge away.

Swapping to an upgraded converter is probably a better value if you can return the charger.

Do you really have an inverter or just a converter? Your converter, if that is what you have, will charge the batteries while you are plugged into shore power. No need to use the charger. If your batteries need charging and you are not hooked up and driving nor are you plugged into shore power then use the charger.

You're waisting your time.

I would 'think' that the on board charger would put out more than 12A. Both chargers could fight each other. I wouldn't use both at the same time.
BTW, I have a Residential Fridge and the Sine Wave Inverter charges the batteries at 55A.