Tips on dealing with bulky/irregularly shaped pieces in drill press?

Get a piece of flat steel or stout osb, and Bolt the head flange to it. Then grip the flat stuff vertically in a vice on the drill table. Block up underneath the holes you're drilling at that point.

Start with a center drill, or better yet an end mill to get a flat face to drill on.

And as mentioned... heat, oil, and left handed bits.

Work slow, save the beer for after the work is complete