It sounds like you're not really looking for a framework but more leaning towards just wanting a library of classes. Zend will probably suit those needs better than the likes of Cake or CI just because of the sheer number of classes that have been written for Zend Framework already. Then you're looking at using a class from a library the learning curve is much, much shorter and shallower than adopting a whole new framework -- it's essentially just a quick scan over the docs (any library or framework should be well documented) or the class(es) itself for the API.

You mentioned earlier that your work partner is against using Zend. Do they prefer another framework, or starting from scratch for each project? Finally you mentioned trying CakePHP but have you tried any other frameworks; Symfony, CodeIgniter, etc?