Hey Jeremy,
From what I've witnessed, there is a script on the vCenter login page that will try to make a call to 'wss://vmware-plugin:8094/?src=client&sessionId=<insertSessionIDhere>&appName=ui&version=2016'
Hit F12 and look at the "Network" tab, do you see a bunch of pending connections to that address?
The additions made by the program (EAP 6.5) were:
::1 vmware-plugin
127.0.0.1 vmware-plugin
Have you tried adding them manually?
I can't guarantee that the same changes will work in the 6.0 branch, but I think that they use 'wss://vmware-localhost:8093/' instead.