Thanks for taking time to look at this.
1) I don't believe I can re-add the nworks UI connection because it is in use to monitor the rest of our VMware environment (single vCenter server) and I don't want to impact monitoring of the rest of the systems if I can help it. That said, I'll try it if nothing else seems to be working I would try it but just to be clear do you mean Configuring the OpsMgr agent (from the Enterprise Manager Dashboard in SCOM) on the nworks Enterprise Manager Collector server, or from the individual collector that runs the VI-AP Link? (Or something else entirely?)
2) I double checked permissions, and we have read-only from the top down for my nWorks/Veeam monitor account.
As for hosts in SCOM, yes I do see the ESX hosts that fall under those clusters as actively reporting in SCOM (ESX Host State shows them) and the Cluster State health explorer appears to have relevant data. Performance charts also seem to be there (I can create reports that capture info on the hosts and VM's on these clusters).
Here's a screenshot showing the ESX Host State which is populated with hosts in the UCS Conf. Cluster (hosts 12,13,14,16,17):