If you can locate a stair-building shop, you can get handrail material in diameters up to 2" in any kind of wood you care to name. there are also component suppliers that sell the stuff.
Stair shops aren't usually in the phone book, but most of them are union. Check with your local UBC hall. They should be able to refer you to someone.
It won't be cheap. In red oak, for example, 1 1/2" diameter handrail typically comes in 16 foot lengths at something like 8 bucks a foot. A shop could certainly manufacture anything you might want diameter- and material-wise, but it'll cost even more for them to set up their shaper.
If youre lucky, someone'll have a short piece of cutoff leftover from an installation sitting around that you could get without buying a 16 footer. Oak, maple, and cherry would make a pretty stout shaft, and those are really common.
If you feel REALLY motivated and own a stout router, I could write out a detailed set of instructions on how you could create your own shaft from raw materials. That would require a few tools, however, and large diameter router bits run about $80, usually.
You might make a few calls to some local custom cabinet shops in town also. Pricing might be competive to the stair shop, and most of 'em ought to be able to handle building a beefy shaft with the tooling the've got.