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I ran into the issue where theme functions in a newly installed module would not be picked up. The theme cache would clear fine, but (I think) the module_implements() cache didn't, causing the new modules theme hooks to be unregistered.
My suggestion is to add a hook_flush_caches() implementation with just
apc_clear_cache() as body. In this way, there is at least a method whereby the cache can be cleared. If this is undesirable, perhaps adding a separate Clear APC button somewhere is a better idea.