Lost Sheep, I ran all the cases through a standard Lee full length resizing die and bench-mounted press before reloading them in order to eliminate the "set" from the previous rifle's chamber.
Your point about chamfering is well taken - I will pay more attention in this regard next time around. Both the chamfering tool and the primer pocket cleaning tool will fit into the box the Lee Loader comes in, which is handy!
The bullets I was using were .312 factory 150gn from Hornady. If they're oversize, that would seem to be Hornady's problem.
As for orientation, how does one ensure this with the Lee Loader, given that you are dropping them "blind" base-first into the loader?
All stuff to bear in mind for next time. Thanks for the hints, people.