I knew about the steel part, but I was wondering, why add the brass? For corrosion resistance and the surface lubricity to aid with extraction?Pretty much all shotshells are steel based now with some brass flashed on them.
In American made ammo, the difference between hi and low brass has always been a marketing tool to sell to the hunter. High brass = magnum loads, low brass = dove loads which isn't true.
In reality I've loaded thousands of "magnum" shells with low brass. The chamber contains the pressure, not the .008 brass. Some shotshells ae pure plastic with zero brass.
Every shotshell I know of now can be picked up with a magnet. That is what I use when busting some clays. The AA shells can be picked up but they have more brass than steel and don't come readily to the magnet.
Polishing up the chamber like you suggested may work very well.
If it doesn't, you've at least eliminated that possibility and can move on to something else.