Breech closing issue

[TD]

I have a VH Parker 28 ga circa 1920s. I'm having trouble closing the breech with certain ammunition. The chambers measure 2-3/4". I can't use any kind of Remington ammunition and Winchester AA. Some of the Winchester field loads work fine. I've tried RST 2-1/2" shells and some work and others don't. The problem seems to be the rim thickness of the shell. I'd really like to hunt with this gun but it's frustrating when some shells allow the breech to close and some don't. I'd appreciate any advice or ideas to remedy this problem. I might add that a reputable gunsmith said I would need to ream the chambers but I don't understand why the extractor couldn't be machined to accommodate all ammunition. Thanks.