I must have missed this thread when it was first popular, but since it has been revived and I had the late opportunity to read through, I'm very glad I did!
I really hate to contradict Bogs (isn't that a crime punishable by death or something??) ;) but I have to say that you
SHOULD bother trying to drill them out.
To start off, I picked out a drill bit marked "3/8" from my "el cheapo" brand masonry bit set. It actually measured something like 0.390 to give 3/8 some nice clearance but since that was what I wanted, this worked great for me. Then I sharpened the carbide tip on my silicon carbide grinding wheel, I've usually seen them in green. "Don't bother" with aluminum oxide, usually grey, as it will hardly scratch the carbide tip! I ballparked the angle, but it was pretty close to the dull angle that was supplied on the drill bit.
Here's the setup. It doesn't get simpler than this, folks:

I used a very generous amount of heavy weight oil and turned my mill down to it's slowest speed - 180 RPM, I think. After I saw it starting to cut and my ears were starting to ring from the "chalkboard-like" sound, I stopped and put on some ear muffs! Then I went back to it and kept the bit cutting with moderate to heavy pressure.
Here's what it looked like about 1/4 of the way through:

Note that my particular block has holes through all sides so the center is a bit bumpy to go through where all the holes cross. After going all the way through, this is what the bit looked like:
(Sorry, cell phone camera wouldn't focus this close so I hope you get the idea. There was definitely more carbide there when I started...)


But, there was still enough of a tip left there without doing anything to it that I thought I'd try drilling through the hole on the other end as well. I used a bit more pressure this time and I think it went smoother. I let up a bit when going through the center to avoid ripping the carbide off. I suspect that a better-supported tip or different grade of carbide might chip less.
The top stud is threaded into one of the existing 3/8-NC holes, while the other two are now clearance holes for the same studs.

My advice if you want to try this yourself is as follows:
1) Have a reason and only drill the holes you need. You are likely to ruin some bits getting this done.
2) Have extra bits around. You are likely to ruin some bits getting this done.
3) Wear safety glasses. You are likely to ruin some bits getting this done.
4) Your 1-2-3 blocks might have been hardened better than mine. You are likely to ruin ..... ok, you get it by now, right?

Fun little experiment for the evening. I hope this helps someone out!
-Sparky