The problem with magnetic SS is that some is as valuable as non magnetic and some is not. The key is in the Nickel content.
Chrome is a hard layer thet will not scratch very easy and if penetrated you can see it as a definate layer, typicaly with a copper substrate. It will flake or peel If proberly abused. Try a hammer or Use a file and a 10x loupe. You are a treasure hunter you have a loupe right?
With the magnetic SS you have 2 main categories: 400 series and Precipitation Hardened (PH), 400 series is not worth any more than steel, PH if identified as such is worth the same as 300 series or very close to it.
I believe SS cookwear is PH SS. You may find it profitable to invest in a small device for clasifying SS, hand held and similar to a lazer thermomator. Try MSC Industrial or EF Baily they should have them. There is a bunch of PH SS used in industry.
The real trick here is to educate your local scrap yard as to the value of the scrap that you generate. If you know that you have enough to make it worth while then take them to task on this one. If you have quanities of the stuff on a regular basis and they won't change their price then you need to find a yard that will play ball and let your regular yard know you will take your business elsewhere.
Any high Nickel content metal should carry a higher scrap value so do your homework.
Fact not Theory
Jeff