in general there is nothing weird with multiple IP addresses and 1 MAC address. as long as that MAC address belong to one device / interface.
but you are working on a cloud service so MAC addresses are often manipulated by the cloud provider. on cloud services i usually "ignore" layer 2 and lower. and i seriously doubt the MAC address situation is causing a slow javascript download (but not other things?).
the test seems quite easy, shutdown the second BIG-IP and see if the situation changes with only one MAC address.