Or the case is to short or chamber long and the extractor won't go over the rim.Of course the extractor works with the bolt out of the gun, but it does NOT work with the case is centered in the bolt face as it is when in the chamber.
Your rifle doesn't extract. That means the extractor is not working.
What JBelk said about the extractor being bad makes the most sense to me. I would start there before I ever worried about the headspace. It seems the most obvious remedy,. Take it to your Smith, I'm sure he has put in more than one Remmy extractor and has a Go guage.The extractor does NOT work if it doesn't pull the case from the chamber. No matter how it acts otherwise. If it doesn't work IN THE GUN, its useless and needs repair.
The Remington 'Three rings of steel' extractors are a very complicated part that's had engineering and production problems since the prototypes in 1946.
They ARE spring steel, but with very little 'temper'. They only have to work .021-.026" so can be very hard and brittle and still last a long time. It takes very few overly-hot loads to crack them. (most seem to be broken by trying to pry it out so it works better.)
There are at least four different variations of those extractors and all of them are tough to install correctly.
I really hope the newest Remington continues parts and repair. That's one that's commonly broke and seldom repaired as good as new.