David, as others have said I'm happy you weren't injured. Thank you for posting.
I shoot a lot of Short Tens both for hunting and clays. Regarding Federal 10-gauge hulls, they do of course have a paper base wad that's more/less held in place by compression at the bottom of the hull. I've attached a pic of a sectioned 10 gauge Federal hull. Note that the plastic wall is crimped/held by the rim, but the base wad is not. I discard these Federal hulls after 4 loadings (to include the first factory loading if I am using once-fired hulls from RST shells). And I've developed the "trap shooter" habit of blowing through the barrel(s) after each shot to see the typical smoke at the muzzle and thus check for a base wad that's come loose. It's not commonly understood but when a shell is fired a partial vacuum is created in the barrel when gas exits the muzzle, and that can "suck" a loose base wad into the forcing cone or barrel. Shot seems normal and an obstruction is in place for the next shot.
Most of my Short Ten shooting nowadays is with the olive-green Remington hulls that have the low plastic base wad.
