The back end of the lathe spindle is rarely used unless one uses a collet drawbar or hand crank for low speed.
that being so, and recognising low volumes of abrasive dust from diamond wheels, how about having a semi permanent grinding wheel set there, it would be a little bit away from the lathe bed? It would need a reasonably accurate expanding mandrel to mount it on and a decent catch on the change wheel cover to keep the rest in position.
On the other issue of abrasives and the lathe, does anyone know if all abrasive particles settle in the suds tank or does some of it get recycled in the coolant flow? The splash tray must attract lots of filth given its perpetually sticky state and on my lathe that gets rinsed over when using the coolant liberally.
( I might run some of the suds through a filter paper to see exactly what comes back up from the tank.)