I use Helprace by Satisware. It doesn't tick all of your points since you have slightly different needs, such as an on-premise helpdesk.
Of course, I don't have the need of an on-premise servicedesk, and user engagement through a knowledge base, community and a feedback portal is more important to me. I also don't see a point in comparing anything to Zendesk simply because Zendesk is out to lunch with their pricing structure..