@Dirt Machinist I really appreciate your experience with Hydraulic cylinders, and the hard chroming. I have used hard chroming once to repair a part [at] Jager Industries, it was quite expensive, and would not be appropriate for a Morse taper. If you hard chromed it, you would completely ruin it. It would never hold a MT [edit...."taper] ever again properly.
With a Standard Modern lathe, there's a good chance it has a hardened and ground taper
No Morse taper is hardened. Not on a Harding, Standard Modern, LeBlond or any other lathe. If it were hard, it wouldn't hold, not under the pressures of drilling, for instance. Unless you think Rc40 is hard - and that won't hurt a good HSS reamer at all.
There is series of techniques for concentrically reaming a tailstock, you don't just shove a reamer into the tailstock and have at it. The burrs in the tailstock don't usually interfere with the process, but they are easily avoided if there's a big one.
It would be silly to reproduce Connely's writings on this or try to describe in short what it takes months to learn as a millwright. Suffice it to say that the burrs on a tailstock in no way impede the correct reaming of the tailstock, if approached correctly. In short, if it is really bad you have to start with a roughing reamer, followed by a finishing reamer. And it does not 'push' the reamer out of true.
For your information, Precision Spindle will hard chrome the
outside of a spindle, not the Morse taper,