That's a really nice looking lathe. Looks like it hasn't been broken in yet. Sometimes it's better to slip the snap ring to a nearly stupid location, to get the clearance to undo it... I'm sure you've tried everything, though.
-- One last resort on one machine was to score the back of the snap ring with a dremel (mind the abrasive dust) and break it, and replace it with new. There wasn't any space between the gears to use any kind of snap ring pliers. An assemble-only fixture!