I do mine the same way. You can see from the photos but might to be good to note drill in the flat sided blank before the stock has been shaped. Whole lot more difficult to work on a finished stock. Not impossible but best avoided.

I do some deep hole drilling too long for my lathe, Lamppost mostly. Some heavy Fishing Rod handles 50 80 100 130 lb class. . Can be done nicely in a drill press. Thin tube chucked in the press. Plumb Bob strung through the tube indexing on a board that has a hole to receive a lathe center. Set the blank up between the quill and center. If real long ,You can reverse the blank and come out near perfect drilling from each end. If you don't have a lathe press is a good way to go.

Just finished a Lamppost out of 8x8 stock 10 feet long in 3 pieces. All drilled in a press, square before the post was turned round.

Boats.