My experience is that difficult extraction with steel headed shells is more often encountered with generous chambers than tight ones.
Expansion into extractor grooves is common.
Sharp and narrow extractors as found on many older repeaters does not help either. Nor does a rough chamber.
This is not a problem exclusive to older guns either. Mossberg guns of current manufacture sometimes have problems with steel headed shells right out of the box. I was trapped in a duck blind for a weekend with a friend shooting a brand new 3 1/2" Mossberg and we drove each fired shell out with a stick.
That said, the Herters and other euro brands loaded in Cheddite and Fiocchi hulls run fine in 'most' guns.
My Italian made automatics love the stuff.
The bolded part is pretty much what Ithaca Gun in Ohio says also, for $150 they will convert an older finicky 37 to eat those thin base hulls:
"The problem you are experiencing is something we have developed a fix for by welding the extractor notches shut and re-cutting the notches to establish a better seal of the chamber wall on the entire brass side wall. The problem only seems to have presented itself in the last 10-15 years with the use of cheaper and at times thinner materials being used for the shell brass."
Of course as you also mentioned a clean and polished chamber helps and is the first place to start, and is a lot cheaper.
I reload the 16 in 7/8 oz. for my fixed breech guns with Cheddite hulls which are different hulls than the Herter's which are also Cheddite. The Herter's are a thinner hull all the way around. Never had a problem in any of my 37's with the bulk Cheddite skived hulls I reload, even in my prewar guns.
I picked up a dozen flats of the Herter's in 16 ga. when it looked like they were going to be hard to get and they started selling them by the box instead of the flat. I use them in my new style A5 Sweet 16 as it takes a full 1 oz. load to eject consistently. But some of the shells from the last batch of Herter's fail to eject consistently, which never happened before. So I have taken to loading a Federal first, which always ejects, and Herter's for the second shell on doubles so if it hangs it doesn't matter. I have read of a few others also having issues with some of the last batch of Herter's before Cabela's discontinued them. For $5 a box I would still pick up all I could get my hands on though.
Just got a text from a friend that Fleet Farm has Gun Clubs on sale for $5 a box right now in 20 & 12.