Its easy enough to tell that your buffer was owned by someone who was either a high-order professional in the polishing trade, or a seriously capable amateur.
The use of a 'tapered thread buffing spindle is commonly found on much smaller buffing motors. Its purpose is to allow 'quick change' of fabric buffing wheels, most commonly cotton.
That 'shaft extension' may or may not be an original optional Baldor part.
I would tend to suspect that it would have been shop-made, to allow the use of 'goblet buffs' in the interior configuration of a workpiece.
My first thought would be that you have a very desirable tool, expensive to replicate, and, should you not have need for that capability, there will be someone who has such a need, would be very willing to trade you a 'standard configuration' buffer....plus a little $... for yours.
If its what I think it may be, it could be quite difficult to remove. Its quite probable that the shaft extension is internally tapped 3/4-10 to match the original spindle. It may or may not have been assembled with Loctite in the threads.
If you wish to try to remove it, you must.....in my opinion, anyway......be very careful to avoid damage, as it may be very well adhered to the original spindle.
You might try by making up special 'wrenches', blocks of a good hardwood, such as hard maple, bored to the spindle size, and split, with a 'clearance' of 1/16 to 1/8" then cut down on one of the blocks. The blocks should be drilled for clamping with suitable bolts, with a long steel flat-bar handle, in such a way that the blocks will clamp firmly to the spindle on one side, and the spindle extension on the other, and the handle will provide leverage. (this is analogous to removing a rifle barrel from its action without scarring it)
You may need to warm the spindle extension to remove it. If you do this, take great care to warm it uniformly around the periphery of the extension, to avoid warpage.
cheers
Carla