+1. Or, if the round posts are a little larger than the square post you'd otherwise have, trim the post to fit the flanges on a standard Simpson. You should be able to do something very clean.If you use pressure treated posts you can always flag pole them right in the concrete. Just make sure their high enough to stay clear of standing water. Also a regular Simpson bracket would work too. The flanges are probably small enough to just bolt on the sides without issue.
A 6" round cedar post isn't quite as strong as a 6x6 square post. Maybe it doesn't matter in your case, but around here, if the plans said 6" square, an inspector would say no to 6" round.the posts are currently 6x6 cedar. They want them replaced with the same size cedar logs. The posts there now have no base at all and that is why I am replacing them.