UPDATE: I was digging through the usb_descriptor.c file for the MQX USB stack and I think I may have stumbled across the solution.
This should have been obvious but it's kind of buried in the stack. There is a manufacturing ID string, product ID string, and a serial ID string that are all part of the USB descriptor. It seems that the serial number string should be unique for each hardware instance running the USB stack. The exact section of code that defines this string is:
uint8 USB_STR_0[USB_STR_0_SIZE+USB_STR_DESC_SIZE] =
{sizeof(USB_STR_0),
USB_STRING_DESCRIPTOR,
0x09,
0x04/*equiavlent to 0x0409*/
};
So the default serial number is "0x0409". When I changed that to a unique number for my second device, they both instantly started working at the same time. I was able to open two terminal sessions with no issues. So it seems the driver is fine and will support multiple instances. I hope this info is helpful to someone.
As far as the device not starting error on the ASUS board, I'm wondering the default MQX vendor ID (2504) and product ID (0300) are perhaps in conflict with something else in that system?