Thanks Elliot! I’ve contacted Gesswein Canada and I think figured out which of this arbors might work with my machine. 
Thanks Kay! 
Thanks Don! I have the hubby working on a solid wood base that will incorporate the dust collection hoods, that will be bolted onto a very heavy workbench bench (also courtesy of my handy man 
).
Hi Roy,
I’ve seen a lot of spindles that will fit the 5/8” shafts, just not any that have deep enough holes (not sure how else to describe it?) so that the set screws will not encounter the inch or so of threads on the end of the shaft. 
If I cut off the threaded ends of the shaft it would be with the intention of making it fit a tapered spindle which would be what I thread the buff on to. None of the jewelry buffs I want to use come with a 5/8” centre hole (I’ve only found huge 8” coarse cotton industrial style buffs that come with 5/8” holes).
Hi Don,
I did wonder if cutting the shaft shorter might alter the balance of the machine, but people seem to attach all sorts of different spindles of different lengths onto polishing machines all the time without throwing off the balance as long as they’re centered well?
For instance I’ve seen machines with a long tapered spindle on one side that holds a couple of separate polishing wheels, while the other side of the machine has a short spindle that just holds one wheel and they seem to run okay. I suppose those might be “just a matter of time” situations where an unbalanced load could run alright for a while and then cause problems down the road… 
I did look into the threaded 5/8” spindles offered by Gesswein but they tell me the internal threading on those is quite fine, and the threading on my shafts is definitely coarse so I don’t think they’ll match unfortunately. The 5/8” straight-shaft unthreaded arbors offered by Gesswein would probably fit though which will be what I try first I think.
I definitely won’t be turning on any polishing machine (altered or unaltered) without lots of face/eye protection and standing well back and to the side! 
Hi Rachel.
I don’t think putting the sleeve or the set screw of the spindle adapter onto the threaded portion of the shaft is going to make any difference. Threads are constructed so that their outside diameter is that of the thread dimension…in this case, 5/8ths of an inch. So the adapter should run pretty concentric on the shaft. I also would not worry about the set screw damaging the threads…use a set screw with a somewhat pointed end and you should be able to make it lodge itself into the valley of the thread, if that makes any difference. There it is unlikely to do any appreciable damage. If you encountered any difficulty using the thread again after using the adapter, threading a nut onto the shaft again should clean up the thread easily. This is a buffer, not a precision instrument, and the wheels are relatively light weight, so even if there is a little runout, it should not matter as long as there isn’t a lot of vibration kicking the motor all around. I’d have to look, but I believe my spindles are sitting on the grinder motor threads…I certainly didn’t give much thought to why it wouldn’t work that way. They have been fine over several years of use. HTH, royjohn
Unless the Gesswein folks gave you an actual thread pitch for the spindle you should see if you can order them on spec. Coarse and fine are technical terms which are defined in the Unified Thread Standard. What you think is coarse may be what the UTS calls fine.
A chart of the UTS threads shows that for 5/8" screws coarse threading is 11/inch and fine thread is 18/inch. So you can count the threads on your shaft to see if it is 5/8 coarse or 5/8 fine. There’s also 5/8 extra fine, which is 24/inch.
I wonder if thermoplastic would keep the spindle on the shaft and also allow it to be removed? But then there’s that annoying issue of heat build-up during use.