No matter what you do, it is impossible to clean a used frying pan to as-new standard.
Tip we were given at Kinloss (1970, our only time in quarters). Off to the auction rooms in Forres, where all the "condemned" quarters stuff was sold off. Buy a frying pan for next to nothing (there were a lot of them). March in, put the brand new issue pan in a cupboard for two years, and produce it unused for marching out.
The used pan was a lovely solid aluminium one - we went on using it for 30 odd years.