I pulled the check valve and pump cup from a donor 880 that seemed in good condition. All o-rings were replaced.
That weird hard plastic or rubber buffer makes no sense to me.
Some more detail on the barrel clamp, I found the barrel wiggled a bit, which means that air was leaking past the seal.
Forgot to take a picture, but I ended up lapping the bottom of the clamp w/sandpaper on a flat plate until it made better contact.
The gun wouldn’t hold more than one pump of air after reassembly, which meant that the check valve wasn’t working. So I decided to experiment and heated it and a round bushing up with a heat gun until they were moderately warm/hot. Then I compressed the seal (making the skirt flare out more) with the arbor press and held it until it cooled.
As you can see, the seal on the left has taken a set and is larger in diameter than the non-working seal on the right. I don’t know how long this will last, but the rifle works now and my neighbor seems happy.
Not a bad result for 10 pumps with a premier 7.9gr. pellet.