Did you try, with the Customize dialog open, Ctrl-dragging the buttons you want to your toolbar?

The button IDs are useful for trying to programmatically build a toolbar but I don't think that is what you are trying to do.

Yes, I'm cognizant of how you can move/copy a button from one toolbar to another. But here I'm trying to replicate a command represented by a toolbar button in a menu. It's just that all of my toolbars are already full (i.e., flush to the right margin of the screen), so I can't copy this particular button to any other toolbar without making them disappear into a drop-down button.