I've had "modern" ammo with the steel heads misbehave in Ithaca M37's, both 16 and 20 ga., and in a Model 12 16 ga. I shoot all brass headed Win. AA HS 28 ga. in my M37 28 ga. and they function without issue.
The late former head gunsmith, Les Hovencamp, of the old Ithaca Gun Company cured the Ithaca issues by re-cutting the alignment of the extractor/ejection notches in the barrels. I don't believe he had to polish chambers. His death left a huge void in M37 work. He could fit extra "non-interchangeable" barrels on the old guns without doing the shenanigans that the present company requires. Gil