I must be missing something. I agree that a straight sleeve bored to a taper, slit, and held in a collet or chuck would be a good way to hold this workpiece. But, if the OP is making enough of these parts, a collet or soft chuck jaws bored to fit the taper would be even better. Depth could be controlled with an adjustable stop, or the collet or chuck jaws could be taper bored to a fixed depth only.
It seems to be that the large end of the taper faces in, so there's no way to do that with a collet without leaving the back end open. Soft jaws yes, collet no. However, we still don't know if OP has a chuck with available soft jaws... Regardless, simpler proposition to make a quick sleeve and split or slit it. Don't need a machinable E-collet for that either. If there are hundreds of parts on a repeat basis, something more permanent might make more sense.