CHC, those old but incredible rifles have two common issues, that when combined, create the issues you're getting now.
First, they "wear" on two critical surfaces.
The back of the bolt is the recoil lug and it sits tight against the shoulder of the notch it rests in when the bolt is closed. It cocks on closing and this applies force on both surfaces when the sear is engaged. From what I remember, neither of these surfaces are particularly hard and they wear.
The wears is very slight, but it happens every time that bolt is operated fully, whether a round is chambered or not.
This eventually creates a condition, which you rightly assumed is excessive headspace.
This wasn't much of an issue back in the day, even with a mix of short/long/long rifle ammo as it was all loaded to "STANDARD" velocity pressures with the long rifle, slightly lower with longs, and much lower with shorts.
When shorts and longs were not as widely used, later, and the manufacturers just "down" loaded the long rifle case, they also "up" loaded the long rifle case with higher pressures in cartridges such as CCI Stingers. These old rifles will chamber and shoot thousands of them before having "set back" issues, but they do create conditions where the wear between the surfaces is sped up.
You could do a lot of shooting with that ammo, without creating a "set back" condition or excessive wear.
Usually, when wear becomes so excessive to create the condition you describe, where case swell or crack when they ignite, sometimes even allowing bits of grit, etc to be "blown back" and out of the rear of the chamber, maybe swelling slightly at the extractor slot.
Most of the rifles I've seen with this condition will no longer reliably strike the rim with enough force to ignite the priming compound in the rim.
I suspect this is your issue. It can be fixed by a talented person with a TIG welder and a file, with a lot of TLC in mind.
The other issue, as mentioned above will either be a "carbon ring" which will happen half way up the chamber, from a steady diet of shorts or long cartridges, which will cause a ring of carbon to build up in the chamber. BUT, if this is your issue, you wouldn't be able to easily chamber the longer cartridges, if you could chamber them at all. I have seen these old rifles, both single shot and repeaters, put away in the safe or discarded because of such "rings"
I don't believe you have a "carbon ring" issue, but a wear issue on the rear of your bolt and the recoil shoulder on the receiver.
If wear is your issue, it will be noticeable. The surface of the bolt handle which rests against the recoil should be flat right up to the bolt body.
When they're badly worn, it's quite obvious.
