Mild stuff means that these loads are fairly "dirty". They don't slam the case mouth against the chamber walls providing a good deal against blow-by, so you get a pretty gritty chamber. Then, when full power stuff is shot, the brass does slam against now gritty chamber walls and is hard to extract. It's plausible.
To confirm, give the rifle a good clean and shoot the full power stuff first. If there are still extraction issues, it's something else. Examine the chamber closely. Are there any tooling marks that might hang onto the brass? Are there any pressure signs on primers. You know, the next usual suspects. If instead, all goes well, only shoot the good stuff after the Cowboy stuff after you've run a bore snake through it a few times.
