Ken,
I think it worthwhile to drop a footnote here on morse tapers. They are not, unfortunately, all created equal. I found this out when I bought my JET home only to find that the TS taper had a slight bump in the interior that prevented the live center from seating properly and aligning with the drive spur point; they [the points] were off by a good .004. Now when spindle turning between centers, it's not that big a deal because you'll turn away the ghost of the slight eccentricity, but with a faceplate mounting, the TS live center point will scribe a circle and its bearings will wear much more quickly. The cure was a No. 2 morse taper hand reamer. A [nuther] tool, about $26 from ENCO, that you'll rarely use after the initial application if you do things right. Looks like a 6" long, 6-fluted router bit that is CAREFULLY inserted into a morse taper and LIGHTLY & GENTLY turned by hand (and wrench) to remove ANY bumps, galls, and other imperfections in the female taper's surface. DO I need to say that the LATHE MUST BE TURNED OFF when you do this? 😱
I judiciously applied a reamer to my JET (1236), and the points met to less that .001; way good enough for a wood lathe. I also found a stray burr on the TS taper of my Stubby 1000 that prevented the live center from seating properly; taper applied and the points (after truing) match to less than .0002.
The reamer is not for frequent use however, as it will tend to bore out the taper. You should use a rubber taper cleaner (Packard sells one) that removes a dust or grit from the taper before an appliance (center, etc.) is inserted to prevent scoring or galling of the taper. Do NOT use abrasives to ream or clean a taper because the fractured grit bits will imbed in the metal surface and cause further damage.