Thanks for responding! I stopped work on it yesterday so I could approach it with fresh eyes today, and found the answer. I have the following settings:
Link on main categories: No
Only display categories with products: No
Part of the problem was I don't have all the inventory in the system yet, so there are some unfilled Categories at the moment. If the Category is empty and "Only display categories with products" is set to No, then the Category will be linked to. But if the Category is not empty, it won't be linked to, and the accordion behavior displays appropriately.
So the functionality of the module I built today is acceptable as-is. Ideally I'd like to have Category not act like a link even if it is empty - but that is not a mandatory design requirement.
Thanks!