Rather than offset the lathe tailstock when turning tapers, after it has been adjusted to accurately turn work between centers, make up an offset tailstock center as shown in these plans.
Obtain the center of your pipe stock quickly and hold it easily with this tail stock pipe center lathe attachment. According to the plans, this attachment will accept pipe from 1/4 inch to 4 1/4 inches.
If you are looking to make a lathe tap holder to speed up the machining operations, these are the plans. This holder for taps on the lathe will make changing operations faster.