Dennis, I have a NIB 345 and your post made me curious. So I dug mine out to look at it. It has the round drag knob. I also posted the owners manual that is with it which also shows the round knob. And if I am reading the numbers correctly, it was published in 1983. And in looking at the 1990 and 1992 parts catalogs you posted, they also have the round knob. So a fun thing to ponder about the star drag. If I had to guess, I would pick Johnson put it on using up parts at end of production run. Not sure why someone would switch out round knob for the star. But who knows.
Gary, I would offer up that Dennis is the most prolific master of reel collecting and finding various versions!