Andrew was pretty damn comprehensive, but incorrect IMO that you want lateral float on the upper pulley, since you're friction shifting (I don't even like it on indexed). Switch the Centeron-G pulley to the bottom, I reckon.

Also, I think cale is barking up the wrong tree; I have a hard time seeing bent or worn chainrings as the cause of your issue.

Here's what I suspect may be the cause, since pretty much the same thing happened to me when I switched to 9spd: excessive runout in your freehub. If you hold the cogs and spin the wheel, any oscillation should be barely noticeable, if at all. Mine was as bad as a crappy freewheel hub, so depending on where in its rotation the freehub engaged, the cogs would be anywhere from zero to a couple of degrees out, resulting in intermittent autoshifting.

Drove me nuts until I found the cause; since you're running friction shifting though, that rules out a whole class of issues I wasted a week or two trying to sort.

If it's a Shimano hub, you can swap out the freehub body pretty easily; pull the axle and use a 10mm allen key to get it off. There are two kinds of spline attachment it could be, and make sure to get an 8/9/10spd HG one.