Does this project require the core material to remain wood? I would create a
makeshift lathe to bore the 3" core out all together, create a 1"dia x 3"
helix, wax core spiral, set it into the core, cast one of the new plastics
over the core, melt the core out, and then cap the ends with a wooden cap on
either end. It would be so much easier than trying to bore a 3" Helix with a
1" bore through solid wood. The casting materials that are available are so
diverse that you are bound to find one that will perform the task needed.
And using this method, you could actually make the helix from metal tubing
to remain within the casting for real strength. Without more information,
it's hard to take it any further than a very general idea.
Hope this adds to the pool of ideas.