An update on my progress.
Stopping the service VMware USB Arbitration Service in the Services section of Computer Management allows my USB devices to be properly recognized (stopping this service also requires stopping the service VMware Workstation Server). If just the VMware USB Arbitration Service service is restarted, the USB devices continue to work as expected. Next, restarting the VMware Workstation Server service will cause the host to fail to recognize the devices properly.
So, as a workaround, these two services can be stopped when you are not using VMware Workstation in order to properly recognize your USB devices. VMware Support is continuing to work on exactly why this is occurring.