Looks like a good project on the go! Regarding that hole through the butt stock - not sure if you have that done or not? I found that with deep holes, often the bit likes to follow the grain in the wood - does not really matter where you start - comes out where not expected. One solution for me is to drill in part way from one end, then flip around the work piece and drill in from other end - that way my "start" and "finish" holes are where I want them to be - trick then becomes to get those two holes to line up inside - sometime do, sometimes do not - errors within that "bore" do not seem as "project ending" as with a hole coming out in the wrong place. I think the long hole drills for metal sort of "guide" themselves to stay more or less straight - not really the same when drilling into wood along the grain of it - like you would be in a LE butt stock.
Another "trick" that I have done is drill the first hole at a way smaller diameter - get that small hole connected from start to finish - then large bit to finish size - seems to act more like a reamer, rather than a drill bit - tends to want to follow the existing hole more closely than the grain. Your mileage might vary. I have a longish 1/4" diameter bit that I have used for pilot hole - many bits used here had pilot noses ground to them to follow that 1/4" hole - not real certain if that pilot nose is needed on the larger bit or not.