Posting a follow-up answer to my question.
I believe that redundant links per chassis is not the optimum design because you would need to running spanning-tree. In fact, it's recommended to configure port-fast on the Catalyst port and disable bridging on the CSS altogether.
I also realized that trunk ports and spanning-tree are not necessarily required together so, in my case, my 2 server-side VLAN's can be trunked to a Catalyst using a single port.
Cheers,
Dan