In order for the 5-6 browsing methods to work ideally, every resource would need to be available to every category redundancy (the different categories that mean the same thing). How would we guarantee that?
I'm not sure what you mean, although I agree that forcing a redundancy will quickly undermine any proposed structure. I'm not proposing separate categories that mean the same thing. It's more about how to name a category so it can encompass a broad range of sub-categories. An example is Category:Schools, colleges, institutions or Category:Subjects and topics.
I've made a first proposal for these top categories at Workgroup:Categories/Proposed_map. Maybe you could provide an example of the redundancy using one of the elements in this proposal.