More information... All hosts are connected to a four-switch stack of Cisco Catalyst 3750-G's. All ports are trunked (8 for each server). No etherchannel is being used.
I did a "show mac-address | incl [virtual mac of VM]" and saw that when I moved a VM to one of the new servers, the switch did NOT get notified that the VM should be associated with one of the physical ports attached to the new host (i.e. it was still showing as being seen on a physical port connected to the host that I just migrated FROM). If I migrated the VM to any of the existing hosts, the switch updated immediately and showed the MAC address to be on a different port.
I am going to do some digging into the settings that have to do with notifying the switch, MAC/ARP tables, etc. I thought that was all managed at the dvSwitch or Port Group level, but maybe there is something at the host level that is causing me an issue? Worse yet, I hope it is not related to the particular NICs in use on these servers. They are different than what the existing servers were using. I could do some testing on that (the hard way) I suppose. I am running out of ideas, but at least I think I have a bit more information than I did.
Any other thoughts?