A little more work last night, had me fitting a couple of pieces of tube to fit between the front and back plates.

Use of the lathe allowed me to cut them very precisely and fitting them has made a very sturdy unit, which without them was quite flimsy.

I have a vague feeling that I might have swapped the covered over as I picked them up off the bench. The good news is that it seems to have resulted in an even better fit than I had yesterday.