Diggy, I did a string though on my first attempt with no problem. I found the largest drill bit that would fit through the holes in the bridge and used the bridge as a guide to start the holes on the face in the right position. Once I had them started (1mm -2mm deep) I used a drill block to drill them all half way through the body. Then I drilled both e strings all the way through and used the bridge on the back side to pick up the position of the e strings and align the remaining string at the same way.
The key is to get the entry points on the faces nice and even and the bridge can be a guide for that. If they’re a bit wonky in the middle of the body no one will see.