Points to think about:
If you cook at temperatures over 500 F, normal cooking greases and oils are at, or likely to soon reach, the "flash point." Hence, you are creating a serious risk of a grease fire and also are denaturing foods and greases, and thus emitting smoke and vapors that are likely hazardous to your and your pet's health, regardless of what type of pan you are using!
PFOA-like chemicals are added at very low concentrations to powdered fluoro-polymers to help the non-stick polymer powders adhere, in an even layer, to recently stamped, cast, or spun pans, prior to "baking on" the non-stick polymer finish. During this baking-on phase of cookware manufacture, the bulk of residual PFOA-like emulsifiers are driven off to a fume vent system from the high temperature manufacturing ovens. That is where vapor controls are needed to reduce occupational exposure.
The widespread bio-accumulation of PFOA and PFOA-like materials in multiple warm blooded species around the world is unlikely to be significantly attributable to cookware. Not all societies even have access to non-stick cookware! We must look to other PFOA like material end uses to determine where the significant animal exposures are coming from.
It's time to stop the cookware/PFOA exposure myth spreading, and focus on the real exposure risks.