Thanks for all the help! I'll try a different headset and see how that goes.
You could try an expanding epoxy. We had a NOS Casati in the shop about 10 years ago and a king headset just slid in with no real force. It seemed to have worked, though the last time I saw the owner was 5 years ago.
@kjlem started
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Thanks for all the help! I'll try a different headset and see how that goes.