Another way to do this is to make a double-ended MT2 arbor – ie 2 make tapers back-to-back (assuming your lathe h/s is MT2 as well). It may be possible to do this by joining two off-the-shelf MT2 arbor blanks, but I made mine from scratch. You first chuck some 3/4 free-cutting and turn the best MT2 taper you can; then remove it from the chuck, remove the chuck, and mount the workpiece in the h/s socket by the taper, holding it with a drawbar. Now turn the second taper MT2 and also drill and tap for a drawbar.
Then bore an MT2 hole in the spindle stock material and ream it to size/finish. You then fit the double-ended arbor in the h/s, and mount your blank spindle on the end sticking out, hold it by a drawbar (ie.a bolt) and turn the outside to be concentric with the MT2 socket you just made. Sounds long-winded but it didn’t take me too long and it all worked. If I can find it I could lend you the double-ended arbor I made?
John.