In the pictures I can see where a hole seems to want to 'slide' into it's neighbor. That exactly what you get with lame bearings or a flexing bit. The sideways pressure of cutting overlapping holes is moving the bit tip.
A couple possibilities: use the shortest possible bit, it'll flex less; keep your work as close to the head as possible - you'll have less movement of the chuck; better bits - harder, more rigid, sharper; a better drill press.
Slowing down is a must - give the bit time to do it work. Also, check your RPMs - your press should have come with a table of suggested speeds.
A pic of these bits you describe?
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