Why do I get a taper when turning?

[Robin Hewitt]

taking off a moderately fine cut, if I reverse direction the tool digs in and cuts deeper, yet I can't detect any significant movement in the slide itself.

I like guessing games :dance:

It's a Vee bed, n'est ce pas? If so I'd look at the saddle bearing face opposite the Gibb strip. Has it worn into a bow? If so no amount of tightening the Gibb will stop the saddle twisting and you have some scraping to do.