I sent a PM, but I think this info may help someone else, so I'm posting on the forum as well:
I got lucky drilling the hole, that's a fact.
I lined up the wood so that the grain was oriented how I wanted it, then I squared up the wood and center punched it on both ends for my pilot drill. The pilot drill is (I think) 1/4" diameter by about 12", which made it too short to go through the entire stock. Also, the throw on my drill press is about 4", so I kept having to drill down, reset the table height, and drill again. Then I had to flip the stock over and drill from the other end because the bit wasn't long enough.
And that's where I got lucky. The two holes actually met up! I didn't expect that, I was thinking some slop is OK, because the 7/8" hole does not have to be exactly in line with the 1/4" hole and it'll still work. The stocks from NEF aren't exact, and the one I have from GSI is better, but also not exact. Anyway, once that 1/4" hole was drilled all the way, it was a simple matter to drill the butt end with a 7/8" spade bit, it self-centered on the pilot hole just fine.
If I were doing this a lot, I would have resawn the wood down the middle and routed a 1/4" channel down both sides. Then I would glue it up and have my dead-straight pilot hole. The only thing is then you have a line down the middle of your stock where the glue-up is. On a laminated stock or a stock with fine grain, that wouldn't matter, but on a very figured piece of zebrawood, it would have been an unsightly glue line.
I haven't had a chance to work on the stock recently, but I will post pictures as the project develops. I suddenly got the urge to do a mannlicher stock for my kids' Marlin 795, but I can't decide if it'll be laminated or solid.