Hi there, Hywel,
Check the tang of your MT adaptor to see if it's hardened and to confirm that it has a female centre.
Assuming the tang is not hardened, mount the MT adaptor on the lathe with its body in the four-jaw chuck and the tang centre supported by the tail-stock centre. Dial in until it's running true.
Then turn away the narrow end of the taper, removing the minimum amount of material, to form a short parallel section just long enough to match the thickness of the fingers on your fixed steady. Fit the fixed steady and back off the tail-stock centre, then turn off the tang, face off and drill and tap the end of the adaptor for the draw-bar thread of your choice.
This procedure is based on that described on page 106 et seq. of 'Simple Workshop Devices' by Tubal Cain (the real one!). You only need remove about 3/8" from the narrow end of the taper shank – there will be more than enough taper left for it to do its job (but do 'remove all burrs & sharp edges' ) .
Best regards,
Swarf, Mostly!
Edited By Swarf, Mostly! on 05/07/2016 15:26:00