Ed, awesome topic, and thanks for the pics.
Anything I can do to help dry out the wood?
Time, and air. You should probably alos put some sealant on the cut ends to cut the chance of splitting. Varnish or knotting liquid will do. Some folks'll use a heat gun to dry pieces out after they stream shape shafts or crooks, but I think you'll do more harm than good with a piece like that
YMMV, but you'll probably be okay if you clean it up thoroughly, shape it, and give it a nice heavy coat of linseed and let it set in for a day or three. Couldn't hurt to wipe down and recoat daily for the same period, then let it dry out after a light wipe down. Should cure on it's own over time at that length and thickness, as long as you keep it oiled regularly to keep the outer layers from cracking. It might take a year, maybe even two for the root ball, to completely season. Might want to wait for a heavier finish or sealer for a few months after that, but I'll defer that to smarter folks than I who might want to chime in. Also, a bit retentive, but if you store it leaning in a corner, try to orient it so which ever way feels like the primary face is down and out. If it curves at all (unlikely, given the stick in question), it'll be in the right direction
If you want to go nuts, or cut a batch, esp. if you harvested any longer pieces (six foot walking stick with a carved softball sized root ball, perhaps?), you can go nuts as follows. Once you've finished barking them, if you decide to, hang horizontally from a rafter in small bundles of 3-4 some place as dry and environmentally stable as you can without being obsessive, garage or under a barn loft, etc, long as it's relatively protected you'll probably be ok. hang from the ends maybe a foot in with a simple loop, you might not need a third loop in the middle, but it won't hurt, particularly with longer (5' +) green staves. Try to give it six months at least, even a year, depending on how arid it is, and when you harvested /how green they are. I wouldn't blow any money on anything to check the moisture levels of the wood as it seasons unless you're gonna do this pretty regularly. Check periodically, every couple of weeks, once a month, to see if there are any cracks or runs forming as it/they dry.
Sorry for the novella, if you have any questions, or want names of a couple of good books on the subject, shoot me an email.