Unfortunately, I don't have access to a router, but I'm cautiously confident I can do it with pilot holes and a sharp chisel.
Bridge has been placed and I've just finished the through-body string holes. Unfortunately the drill press won't reach that far into the guitar's body but my improvised vertical drilling gig worked well (basically a 2x4 with a vertical hole clamped against the guitar body). I've got the two E string holes all the way through pretty straight. The other four holes I started from each side and had them meet halfway through. This was the scariest part but I'm quite happy with the result so far.