Sorry to be 2 years late responding to this post, but I just joined USFG.
I have an original Seattle machine and had the same problem with the ‘slop’ in the index position. Before I discovered what the actual problem was, I faceted okay by keeping steady clockwise pressure on the hand piece – worked but was a hassle. The real problem is that the BRASS index plate has a round 1/2″ hole in it with a key way slot. The STEEL key is in the center shaft of the hand piece, that is the shaft that actually turns. The brass is so much softer than the steel that over time the key way slot has worn and is wider than the steel key. As a result the index plate is locked in position firmly by the arm that engages between the teeth of the plate. But the shaft can turn back and forth by the amount of wear in the key way.
The simple solution of course is a new index plate. Very nearly as easy and much cheaper is to get a center punch. Remove the index plate from the machine and lay it on a very flat, smooth, solid surface. Position the point of the center punch on the index plate, 1/32 inch from the side edge of the key way. Gently tap the center punch to create a dimple in the index plate, which will squeeze the key way closed a tiny bit. By testing the fit, you can make the dimple deeper and the key way narrower if desired. If need be, you could also do it on the other side of the key way, but I would recommend saving the other side to do it again in a few years when the key way wears some more.
There is another post now in this thread that provides a link to new collets that are available.