Counter bored

After several different approaches, I think counter-boring the screw holes gives the best results.  Here you can see the counter-bored bars on the left and the normal screw holes on the right.  

And here's the device I just got to ensure a perfectly straight hole with consistent depth:

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Rockler drill guide

This setup is well worth the money, especially with the 25% Fathers' Day discount (thanks Dad!!).