To follow up on my own question, I figured out a solution. I added three hooks with the following local variables:
# Local Variables:
# eval: (add-hook 'org-babel-pre-tangle-hook (lambda () (setq zz/saved-macro-templates org-macro-templates)) :append :local)
# eval: (add-hook 'org-babel-post-tangle-hook (lambda () (makunbound 'zz/saved-macro-templates)) :append :local)
# eval: (add-hook 'org-babel-tangle-body-hook (lambda () (when (boundp 'zz/saved-macro-templates) (org-macro-replace-all zz/saved-macro-templates))) :append)
This works! The first hook saves the current buffer's macros to a temporary variable before starting the tangle, which gets unbound by the second hook, and the third one uses it on each code block's body to expand the macros.
This feels a bit clunky, because of the need to define multiple hooks, but also because the third hook (and the temporary variable) cannot be made buffer-local, because the operation happens across different buffers (each =org-babel-tangle-body-hook= runs in a new temporary buffer with that block's body in it). So the third hook will remain in effect for any other org buffers I edit in the same session. Since the first two hooks are buffer-local, it will have no effect, but it still feels hacky.
If anyone has ideas for how this could be done in a better/cleaner way, I'd love to hear about it.