Every time I try to use the turntable, it ‘wobbles’ as if the center of the turning action isn’t in the center of the object. I’ve tried to manually position the model to eliminate this, I’ve also tried having different subtools selected at render time in case it selected the middle of a current sub tool, but no luck. Am I missing something?
Does the wobble disappear if you turn off Perspective? If so, then the effect is due to the way ZBrush handles perspective. You can solve it by adding a ‘base’ to your model:
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Append the Circle3D ztool and position at the base of your model, with the center of the circle the same as the center of rotation.
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Using the Deformation>Size slider, scale the circle so that it is just large than your model. No part of your model should overlap the edge of the circle.
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If you don’t want the base to show in the turntable, press Tool>Display Properties>Flip. Don’t turn off the subtool visibility or you’ll be back where you started!
It does have a base, which is larger than the model (no overhanging) but still wobbles. I tried using a disc, (good idea) and it still wobbles. It wobbles weather perspective is on or not. I’ve tried creating a disc by itself, and that doesn’t wobble, but when I append it to the other model, it wobbles, even though the disc is larger than the model…
Anything else I can try?
You could try Transpose Master. Use it to create a TPose combined mesh and see how that rotates. You can easily adjust the rotation center using the Deformation>Offset slider. If you can get it to rotate OK you can transfer the position in as you would a pose. Back up your model first! 
Someone correct me if I am wrong but I believe that Zbrush retains the OBJ pivot from whatever program you created the base mesh in. If you pivot is off center or something in Maya/Max it will mess up your turn table.