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I’ve verified that my Goodwill router does indeed round edges. One thing it does not do is take anything than 1/4” router bits, but hey, it is a $20 Goodwill gamble, so I’m lucky that it turns on.
A nice thing about routers in general is that I don’t need to clamp down a fence like I thought I did, at least for rounding. The part that extends past the cutting part of the router can ride along the edge of the board and keep the router at a fixed distance from the edge of the board.