Now that I have time ...
In the comments for TX Turner's response to How can I fabricate a wooden cone?, there is discussion of using a jig which can make a cylinder from a large blank. Essentially it is a large box with a spindle on which the blank turns. A router rides on a sled along the top of the jig and can progressively remove stock. Examples are in this video and this tutorial. These are for spindles of a few feet long, but I don't see any reason it couldn't be made longer ... you might have trouble with the piece sagging if it's too thin, so you might need to do somethign clever with rollers or the like once it starts getting nearer the desired radius.
This would require that your green wood be very straight, or you'll wind up with a very long toothpick at best.
I would probably start by using a bandsaw with some sort of wedge to trim it into a mostly square or octagonal blank.
Another option would be a dowel cutter. I don't know if there are commercial versions that large, but it shouldn't be too hard to make your own, similar to this one. The dowel is fed through the cutter, spun by a drill or similar spinny device (technical term). I suppose you could alternatively twist it down by hand. Start with a large diameter and work it down until it's the diameter you want.