Projects like repairs on a drill press can take time, patience and a good hammer. I did some research and found a previous expert post that has some instructions for a similar model. I attached that and the schematics for your model from Sears Parts Direct. I also found some additional information and links to videos that may help from another web site. I attached all the links below. Hopefully some of this information will help while you wait for the expert.
I can understand wanting to know how to remove the spindle in the quill assembly.
First you will need to remove the drill chuck from the spindle shaft by locking the quill and using a piece of hard wood to get onto the upper shoulder of the drill chuck and with a hammer tap it down and off.
Next you will need to remove the quill tube from the housing of the drill press.
You will need to remove the handle lift tube from the housing so the quill can drop all the way out the bottom.
Release the set lever on the let side for the quill and remove the retainer that holds the elevation hub and remove hub from the right side of the housing.
The quill assembly should then drop out of the bottom of the main housing.
Then to remove the spindle from the quill you will need to remove the lower retainer ring and washers and then tap on the top of the spindle lightly to drive the lower bearing and spindle out.
I hope these instructions will help with your spindle removal on the drill press.