I used tape on the tube to make it a better fit, though the amount I used to fill the gab was small, the effect was great (it stopped wobbling)

Then drilled two holes 30mm down across from each other. I used a nail to puncture the hard steel surface, then used one of these to finish the job: http://dx.com/p/electroplated-diamond-grinding-rod-set-30-pcs-239638

I connected the two sides with some spare parts I got from an Ikea furniture, but bolts and screws should work as a fine substitute.