Since the splitter did not work how I have another idea. First, you will need to figure out a way to hold the spindle captive. The greatest risk I see with this new idea is if you cannot find a way to secure the spindle you might run the risk of cracking the cast housing of the machine which would be REALLY REALLY BAD. Now that I have that out of the way, secure the headstock. Next, thread a bolt or piece of all thread into the end of the arbor at the outboard end. Working off of that thread rig up some sort of combination of threaded devices that wil get you from whatever size that is to a thread that you can connect to the end of a slide hammer. Next you will literally hammer the poo out of the whole thing to break them apart. Doing this in conjunction with some carefully applied torch heat where the MT of the sarbor enters the spindle would likely help as well. If you decide against this method then I have two more ideas on how to break it all apart. EDIT: Another thought here would be to secure the arbor which would be easier gripped with the hands and use the slide hammer on the backside (drawbar end) of the spindle.
To my thinking the next option would be torch heat. If you are not comfortable doing this I would take the whole thing to a good welding shop in your area. A guy that is good with a torch can apply heat to the assembly and the arbor should break free of the spindle due to expansion and contraction of the steel once the heat is applied. To me heat is a last resort because of the detrimental effect it will likely have on the parts heated. I would sacrifice the arbor before the spindle if given a choice. A new arbor will cost around $100 if you cannot find a used one. But then, who knows; you might still be able to salvage the arbor once it has been broken loose.
I would have the greatest amount of heat centered on the arbor for sure though. If that fails or you do not like that idea the very last idea I have to offer would be cut the arbor in half at the end of the spindle. Next begin drilling successively larger holes into and through the center of the remaining part of the arbor, the MT that is buried in the spindle. Keep drilling larger and larger holes. Stop short of drilling into the inside walls of the spindle. Next take a piece of round stock just a few thousands shy of the ID bore of the spindle and run it through the back of the spindle and seat it against the back of what used to be the old arbor shaft MT. Take BFH and beat the end of the shaft until you finally drive the remains of the old arbor out of the spindle.
None of the options I outlined above are desireable, but that is where you now are. If none of those plans can or will work then I am out of ideas for you. I would rather have the parts out and the ability to make progress on my project than stuck like you are right now. I would hate to have to desrtoy the arbor to get you there, but it might just have to be the way.
Notice the arbors for sale here
http://www.tools4cheap.net/products.php?id=16 if you had to destroy and replace yours. Destrying the spindle instead of the arbor would be a much less desireable alternative to me.