Gentlemen, thank you for your input.
I think I have a compounded problem. There is definitely play in the bushings. I am fortunate in that I have a newer model with a stainless shaft so the play is not caused by corrosion, however, the nylon bushings are definitely worn. To remedy this, I have decided not to buy replacement Tormek bushings and, as I mentioned previously, have ordered flanged Oilite sintered-bronze bushings in the correct size. These should ensure a long-life with no need for lubrication and lovely smooth running.
If anyone is interested, the dimensions measured from my machine are as follows:
Inside Diameter (shaft diameter): 15.98mm
Outside diameter (bushing mount hole): 22.33mm
Flange diameter: 28.00mm (rounded off as non-critical)
Flange thickness: 3.00mm (rounded off also)
All measurements were taken with Mitutoyo dial calipers.
Using this information I have ordered these bushings:http://www.bearingboys.co.uk/OBF162212_Flanged_Oilite_Bearing_Bush-6233-p
The shaft should be a fairly tight fit at that tolerance and I'm hoping the bushings should fit without significant play in the mounting hole. I'll use some medium-strength bearing compound to seat them.
The second problem, as mentioned by Spindle, is a distorted wheel from long-term, asymmetrical immersion in the water bath. The shaft shows no discernible run-out. I have the diamond truing tool, so after I install the upgraded bushings and everything is aligned and locked down, I'll re-true the wheel.
I suppose I expected the lads to look after the Tormek (as I would) and empty the water bath after every use as I requested. They have often scoffed at the slow speed ("Bloody gimmick", "Cheap toy" etc) so I think it will be back to the old bench grinder for them and the T7 will return to the garage for my use.