There have been a couple of helpful suggestions such as replacing the bottom bush or the whole turret kit from a standard car but it doesn't seem logical that either of these would solve a rattle that was there from day one - and on a non-standard piece of kit.
So I built up some courage today and dismantled the fippin thing. Everything appeared to be tight and intact and complete. The only issue seems to be some upward and downward movement on the bottom bush. It's a green poly bush. Please see the pics as a guide to hopefully suggesting a solution?

Short shifter with extended lever and Voodoo knob. It rattled with the standard short short shifter. Still rattles with the long lever. Still rattles with the piece of rubber pipe added to the extender to make it fit the gaiter better. Pretty isn't it? The pipe seems to cut down some of the extra heat from the gearbox though.

Intact upper boot. All bolts were fairly tight. Needs a clean (spilt beer on it).

Side pic of upper boot showing attachments.

Intact lower boot. All bolts were tight.

Fitting below lower boot upside down. Gasket intact.

All seems good apart from the up and down movement on that green bottom bush. Other ones I've seen are white, not green, I think?


Final pic
Sorry this is so long winded but I really am ready to be rid of this damned rattle, if only so I can start work on getting rid of all the other less annoying ones.
By the way, it's surprising how much more gearbox, engine and road noise and heat there is driving the car around with just the bottom boot attached. Yes, this does mean I managed a partial reassembly! I might treat myself to a replacement for the previously discarded sound proofing when I finally reassemble it with the solution you can hopefully provide.