Just received word from F5 support that HP NIC teams that consist of TLB and SLB are not supported by F5 LTM. Also, it looks as if the Cisco switches are doing their job by blocking the ports connected to the second switch. Although it seems a bit weird that this would occur with the LTMs in pass through mode, but I guess the Cisco switch sees it differently. I will team the NICs using Network Fault Tolerance and this should solve my issue with access to the VIPs.
If anyone has any other suggestions or believes otherwise, please let me know. Thank you to all that have helped with this issue thus far.
Nimbostratus