As you've found, you need a pillar drill with a very deep throat to do it easily. I've done it using a drill stand and adjusting it to drill through the hole in the base of it. Start from the top and use the bridge to mark the string hole positions. Then drill the two outer ones all the way through, and the 4 inner ones 3/4 of the way. Then flip the body over, use the two outer holes to position the bridge, mark the inner hole locations, drill about 1/2 way. Hopefully the holes line up (you may need to run a drill through a couple of times in reverse if there's a slight mismatch) and you've got a nice straight line of holes front and back.