Peter,
If i were the shaft, and I was guided in an bearing outside and there would be room to vibrate on the inside, I think I would do just that. Have the one on the outside removed entirely and see if there is any movement of more that 0,5-1 mm of the shaft possible in the inner bearing. If so, it needs replacing. I think Eric from Paperino told me about a similar problem. What he did: Push a new bearing in front or behind the old one. Don“t know if that worked. he told me in winter...
Another thought: Are you sure that these are two bearings and not a shaft tube as a whole that is a bearing throughout the entire tube? These do exist.
Yet another thought: Why not push the inner bearing out from the prop-side with a tube whose diameter fits just into the shaft tube?
The best of luck!
Regards
Alex