You already know why the panels shut off.

Anti-islanding explained the shutdown. It didn't explain what my setup was missing. Once I understood that the panels had done exactly what they were designed to do, I stopped looking for a bigger inverter.

The answer wasn't one oversized battery, either. It was a bank built from several compatible batteries, configured for the loads I actually needed. That was the part I had never done the math on.

One battery can carry one small load. Several batteries, grouped in the right sequence, can carry selected household loads using the power already stored inside them. No new source of electricity. No promise of magic. Just storage sized and wired for the job.

The shutdown was only half the answer. The wiring sequence was the part nobody had shown me.