I'm looking for advice/guidance. I apologize in advance for the
length of this post. Here's the situation. I've got an antique bed
made of oak that is wide enough for a full mattress, but not long
enough. The original design called for ropes to be looped around pegs
inserted into 3" diameter rails around the periphery of the bed.
Then, a feather mattress would sit on top of the woven ropes. I want
to put a full boxspring and mattress on this wood frame. I need to
extend the length of the side rails by 5". The side rails are 3" in
diameter with threaded ends. The threads are reversed on one side so
that when the rail is turned it screws into the headboard and
footboard simultaneously. Actually a pretty ingenious design that I
would like to maintain. What I plan to do is cut the rail an inch or
two behind one of the threaded ends and put in a 5" oak dowel
extension. I know this will require a precise cross-cuts and I'll
probably have to go to my local hardware store to have the cut done
there with their radial arm saw since I only have hand tools at home.
My plan is to join the three pieces (existing end with threads, 5"
extension piece and remaining rail) by drilling a 1/2" hole down the
middle, applying glue and using a 10 or 12" lag screw to join and hold
all three pieces together. I hope this gives enough detail. Here are
my specific questions:

How can I arrange the existing rail and extension oak dowel rod so
they are cut precisely and will make a straight rail when they are
joined together?

How can I maximize the chances of drilling a 10-12" hole down the
center of all pieces so the resulting extended rail is straight?

Is there a better way of doing all this?

Thanks in advance for any help.

Dave