If you can stand the pay and working environment, government (local or state in the US) internal non-safety critical app work may be the safest thing -- you almost never have customers in multiple time zones, or with working days or hours significantly different from your office's that need support.
Program different kinds of software. "On call" isn't a thing for some kinds of software. If it's not deployed to a production server, it likely doesn't have software engineers on call.
I'd aim for a giant bank / financial services company. Some still mandate dedicated Ops/Prod Support teams. It can definitely have it's drawbacks, but you're very unlikely to ever be called out.
Not an answer to your question but I used to keep the on call money in a separate pot. Then over time I would buy something fun from the pot, like some new tech. I found this helped me.
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