Doreen,
I don't have the Axminister Eccentric Chuck, I do have an off center chuck made by one of our club members Danny Hoffman. Great tool, I did a demo at the Southern States symposium with it and did a jewelry bowl with a lid. The lid was done like Hans Weisfloggs with the inside of the lid, I cut rings (on center) and then put the lid on the bowl and secured it with blue masking tape and did the off center rings on the outside, so you could see through the lid. The tape held fine and I didn't have any problems(it also depends on the wood, some are too oily, this was "green" Bradford Pear). When doing demo's or training or off center work I very seldom get above 800 rpm's. I'm just saying you would be surprised how well it holds with a bit of common sense. If you turn like Jimmy Clewes, well then...tape won't do, ever.
Bill