axis alignment

hi im denis
i have 2 boxford tcl
in this period I did a check on the lathe and I checked the z axis if it was perfectly in the center with the spindle center.
but I have found very big difficulties.
I would have several ideas how to align the tip but with processing and modifications.
Do you have any idea where the axis that commands is based, the tip or can you adjust the spindle sleeve?

the conicity inside the tube is cmt5?
I would think to put a pin and do some tests.
from the photos you can see the differences.Attachment 30641 Attachment 30642 Attachment 30643 Attachment 30644 Attachment 30645[ATTACH=CONFIG]30646[/ATTACH