How do I stop metal-bottomed pots squeaking on my gas hob?
Perhaps use a gas ring reducer to lift the skillets or pots away from the original hobs.

There seem to be various shapes and sizes, both bare metal or enamel coated options in various outlets.





As long they don't squeak themselves against either the pots or hob sounds a relatively cheap and easy to replace solution, and don't require changing the whole hob.

They also don't seem to affect stove efficiency or heat distribution negatively in any significant way.

Alternatively you may use some sort of gas ring heat diffuser, though I suspect these will have a larger effect on performance and efficiency.