EV OWA External URL

I suspect the premium client would have the same issue. As you've discovered internally, the extensions will work in both premium and light clients on Internet Explorer. The issue is that the browser cannot be identified as Internet Explorer.

This User-Agent header is why the extensions aren't working:

Mozilla/5.0 (Windows NT 6.1; WOW64; Trident/7.0; rv:11.0) like Gecko

You need to work out why it isn't coming through as Internet Explorer, and you can clearly see the difference in the log files you sent through.

Check if the browser is set to use a different header, or if the firewall is set to change it as it passes through. You can use something like Fiddler to see what it is as it leaves the client and work out if it's on the client or later down the line.

How are they enforcing the light client externally?