The spindle is the easiest thing to remove on that whole machine. There is a 1/4" set screw on the back side of the quill, about 1/4" up from the spindle nose cap. Remove the set screw and then use a drift or a spanner wrench to unscrew the spindle nose cap.(right hand thread) Once the nose cap is off, the spindle assembly slides out the bottom. The "assembly" is like a cartridge, with all the bearings and etc. contained within.
It will probably take you longer to crank the knee down for clearance than it took to remove the nose cap.
To drill it, the best way I have found is to clamp one end in the chuck and support the other end with a steady rest right on the bearing sleeve so it rotates on it's own bearings.
The spindle itself is only case hardened, about .020" deep. I started with a 1/2 carbide drill to break through the case, and after that used a standard HSS extended drill bit. I also drilled from both ends and met somewhere in the middle. Once the hole was drilled to max depth with the carbide, I clamped the extended drill in a tool holder and used the carriage to push the drill. Once you have it set up, it will take about 2 hrs.