For fine adjustment might be like a job for a 'triggerable' DC fuse, or foldback, or current limiter, maybe including a 'held-on' relay that drops out. Many options. There should be lots of circuits around for that. I think the simpler ones are for DC. But they could be used with a bridge rectifier for AC current.
Maybe a small cap across the +/- of the bridge to stop noise triggering it. Not my idea, been around for decades.
There's a good idea in this video
https://www.youtube.com/watch?v=FlRQTPFRUV8
