Many of us proudly refer to the "stuff" we fill our shop with as "TOYS". Your lathe is built light and small to provide an economical way for people to get into pen turning. I expect that it works fine, within the limitations that come with a machine that has been designed with economy as a major design factor. So if you continue to enjoy doing pens, look forward to an upgrade, and in the mean time accept and work around those limitations.
Most carbide insert tools are intended to be used perfectly horizontal, and to contact the blank very close to centerline, +/-. One way to get real close to that height is to set the TR height with no blank mounted. Then you can easily use the center on the TS as your reference, to carefully set the TR height, getting the point of contact between tool and blank right on centerline. Then as you turn the material, try adjusting the TR height slightly. I have found that different heights work better for different materials.