I had the spindle out on the Jet lathe, at work, a few years ago to replace the seals and check the bearings, so this is just by memory and may not be 100% correct.
In looking at my assembly page in the printed parts manual, to refresh my memory, that came with the lathe, #35 is the spacer you have posted the photo of. The chamfer is the side that enters the seal. It is also the side the o-ring #37 will seat against. It is to stop that pesky leak! The oil seal is 70mm ID to fit the OD of the spacer while the o-ring is 60mm to fit the shaft that the spacer rides on.
As for that HUGE amount of play that you have, #43 locking nuts push against the following items in order - #42 50T gear, #38 spacer, #6 outer bearing. The next 2 parts #37 o-ring and #35 spacer are held in place via that set screw to the spindle. They are not involved in the bearing preload that is next. The spacer #35 is actually there to fix the location of the #34 44T gear and the 3 groove pulley #30. They just sit on the spindle and run on the bearing #32. So that spacer sets their furthest left they are allowed to move and the #29 74T bull gear sets the right side. There is a shoulder that the bearing #6 is seated against on the inside of the casting so that it can not go in any further and by adjusting the #43 locking nuts you tighten them to reduce the play and set the bearing preload of the spindle itself.
I think that the above is correct but this was I believe atleast 5 years ago or more.
Pierre