drilling holes that meet, an easier way?

I'm reinforcing a beam/post connection in my barn with some quarter inch thick T-shaped steel plates on each side. I've tacked them in position and have been doing my best to drill squared up holes from each side. The beams (6-1/2" thick) aren't perfect and I'm working up on a ladder, so not quite ideal conditions. The end result is that my holes aren't quite square (perpendicular to the steel) and when I try to put a bolt through it doesn't quite come out the other side through the hole in the steel, though I can see all the way through. I'm close, within an eighth or sixteenth of an inch, and by pushing the drill one way and the other I can whittle away the sides of the hole to finally get the bolts through. With several hours of sweating and swearing I've got three of the 24 I need to do in place.

I'm sure there must be a better way, but I haven't been able to think of it. I could make holes larger than the bolts, say 3/8 or 7/16 for the 5/16 bolts if I can mark them well enough then get the steel out of the way to drill with a bigger drill, but that seems sloppy and I'm trying to prevent additional movement in these joints. Any tricks of the trade for doing this?

Roger, can you make a drill guide with a piece of 2x4 that will guide your drill perpendicular to the posts. If your posts aren't parallel to each other from the side the holes are going in you would have to level your drill guide to each surface it attaches to.

Roger, get a long series drill bit. Engineering tool suppliers have twist drill bits in a range of lengths. If you want to use a spade bit, you can sometimes get longer ones of them too or else weld an extra piece of round bar to the end of it to make it longer.

Still drill part way through from one side and then start from the other side. This way the inevitable slight misalignment gets sorted out without the bit hitting the steel too much. Cheers