When you figure out final centering, it might be better to err on the high side as you can always grind back the tool steel but hard to add on. having said that I think some of the cheapo carbide brazed shank tools stand proud of the square shank section. You could even use like a 60-deg threading point, but better to stick with HSS which you can shape yourself
You can also get round section HSS bits if that helps. It probably would provide more contact area & tool rigidity in your tool holder vs the edges of the square. OTOH its light cutting anyway & maybe more work grinding a flat on the side of the round for your your set screws & trying to get a consistent cutting profile.
What I found is you want a smooth swivel action but no play or it shows up in the finish. Are those cap screws acting as combination axles & tensioners?
If you already know this then disregard, but its helpful to know the distance from the edge of the U ends to the center of your axles. You then add this to the radius when you set the cutting tool tip position so it will turn a ball of a specific diameter.