Reddit mentions of Freud 1/2" (Dia.) Flush Trim Upcut Spiral Bit with 1/2" Shank (75-509)

The roundover bit is the 1/4" one from this set.

The flush trim bit I used is this one.

The flush trimming was hard because it attacked the grain where it was weak. I ended up doing a lot of careful climb cutting to get around the issues, which is no fun. If I were going to produce lots of these, I might give something like this a try. In theory, the shear angle should be a lot friendlier to the wood.

I didn't make the dowel. I usually make my own, but my doweling plate only goes up to 5/8" and since the dowels aren't glued in, getting "close enough" wasn't going to work. I'm sure someday I'll talk myself into a doweling jig like this, but that's a lot to spend on a tool I would basically only use for odd jobs like this.

As it turns out, the commercial dowels I bought aren't that good. The walnut ones are perfect, but the cherry/maple are loose. I have cherry/maple dowel on order from Lee Valley that are supposed to be to tighter tolerances.