Cool project. I hope you don't mind some suggestions that may be helpful - I've done some deep hole drilling myself...
One thing I would suggest is that you bore your hole (Using a long boring bar in the tool post) as deep as you can go before you start drilling. This eliminates some of the inherent inaccuracy of the drilling operation right off the bat.
Also, you might consider adding a bronze bushing secured with set screws a few inches back from the cutting insert as a drill guide. This bushing will need large flats or slots milled on the OD so that only three fairly small areas of the bushing will contact the bore in order to allow chips and coolant to flush past it. Spade drills tend to walk a bit and a guide bushing helps keep them on "the straight and narrow."
Be sure to indicate your bar concentric at the chuck, the steady rest (if you use one) and at the end of the headstock opposite the chuck if the bar is sticking out that far. You want the OD as straight as you can get it. Make a bushing that fits in the far end of the spindle bore to hold it if need be.
One thing that will kill the accuracy of a deep-drilled hole on a lathe is having the tailstock out of alignment - Be sure to use a test bar or other method to check and adjust it before you start.
Go Slooooooow on the infeed - Haste will indeed make waste in this situation. You will magnify any inaccuracy present in the machine, tool geometry or setup by forcing the drill into the material too rapidly.
Here's a website that might give you some related food for thought about what you're working on.
http://www.gundrillingsolutions.com/Pages/home.html Now for my 'wet blanket' input - Having a bar gundrilled isn't all that expensive...