Since none of my four lathes would get down slow enough to do the task, I made my own slow speed lathe using a BBQ motor and a bed a friend, who makes fishing poles and tricks out cue sticks, gave me for a many favors I'd done for him.
Essentially, this boils down to being a tickler for those using epoxy on sticks, and trying to figure out how to keep it where it's applied, rather than sloughing off.
To solve that problem, fishing pole and cue stick builders use slow speed lathes that run clear down around 0-15 RPM.
They have special tracks that are like T tracks woodworkers use, but they can be made by:
(1) Cutting a piece of, say, 3/4" plywood to a length you'd use and, say, 6" wide to use a base. So, if all you are going to do is make canes, it would only have to be long enough to lay the entire cane on the bed, plus a bit for the driving head and tailstock, mentioned below.
Keep in mind, a long one capable of doing a 6' staff can handle a 34" can just fine, because the tail stock adjust the full length of the base. Accordingly, longer allows you to plan for the future.
(2) Cutting two 1" square spacers from wood and the same length as the 3/4" base, minus the length of the headstock/driving head, then, secure them to the outside of the length of the base.
(3) Cutting two pieces of material, say, 3/8" ply 2" wide, and the same length as the 1" spacers. The secure them to the tops of the spacers such that they are flush with their edges and leave a consistent 2" gap down the center of your lathe.
(4) Mount a variable speed BBQ motor to the end of the base you left open (no T track).
(5) Cut four pieces of 3/4" plywood just under 4" wide (the gap in the T-track) and about 6" long (a couple inches longer than the end-stock blocks, below).
The bottom pieces of ply should just fit in the track and slide along it, freely, but without being sloppy. They will be free floating.
The top pieces of plywood will be permanent mounts/bases for the tail-stock.
(6) Cut/Make two blocks of wood about 4" long and just a bit wider than the T-track gap.
One base will accept a bearing to hold the ends of sticks. So it needs to be several inches tall. Different cane and staff makers will have different wants and needs, but tall can handle short, while short can’t handle tall. My tail stock, currently, is only about 5" tall.
The tall tailstock will get a facsimile of a #2 Morse taper (looks, suspiciously, like a straight hole) to hold a bearing.
The other tail stock will just support a bed caster (the double type, so a stick can rest between the two, allowing it to roll easily), so it only needs to be tall enough to allow turning sticks to clear the track.
(7) The head (BBQ motor) just needs a base that will allow its shaft to align with the tail stocks. Keep in mind, up to, say, 1/8" off isn’t going to end the show, but the more accurate the better.
As is obvious in the photos, I was in a hurry and just secured the motor with some plumbers tape. It ain’t broke, so. . . .
I’ll add more details on heads as I collect some more photos.
Meanwhile, I drill a hole in the head the same size as the arbor of the BBQ motor. Doesn't take much friction to turn a stick and dropping epoxy doesn't slow the revolutions down any.