Chamber to die fit is a real thing and getting a good match between the two is part of an effective reloading setup. As you've discovered lack of sizing at the base of the case will result in sticky extraction at the top of the bolt stroke (aka "clickers").
I prefer to measure the base of the case using a vernier micrometer rather than a set of calipers. This is one dimension where the calipers are a bit crude and having accurate measurement to the ten thousandth of an inch can help. I find that I get extraction difficulty if the base sizing is less than 0.0004 between fired and sized brass, and once it's more than 0.0006 it seems to run pretty smoothly. I don't like going too much beyond 0.001 in base sizing, just starts to be a lot of brass working. A micrometer doesn't have to be a super expensive tool, mine is just a plain jane RCBS micrometer that I paid under $30 for. I use it all the time. However, even if you don't have a micrometer you can measure with your calipers to see if you're getting that half thou or 1 thou of base sizing.
As far as fixing the issue, you've got a couple options. Get on the phone and call die manufacturers and ask them their specs on their sizing die for your caliber. Most all of them will provide it (with the exception of Redding). Then you could buy a different die that's a better fit. Second option would be if you have a small base 308 die (or similar) and run the brass through that. It will not touch the shoulder of the brass but will squeeze the lower part of the case. While that fixes the base issue it will likely result in the shoulder being pushed forward as the case is squeezed, then you'll need to bump the shoulder again to set proper headspace (measure before/after, etc). This might last 1 or 2 firings before you need to base size again. Final option if neither of the above works is to just buy a set of custom dies... unfortunatley that can be expensive.
Hope this helps!