Thanks! The second cane (remember, I was making two in case something went awry) went together slightly easier. I think I offset the hole a hair less in that one.
The peg was tapered on the first ¼-⅜ inch, maybe? Also soaked in not-quite-boiling water for a half hour while I got everything ready for it. I had planned to boil the pegs, but decided I don’t have a good setup for that in the shop at the moment, so a coffee cup full of water from the stove would have to do.