I can't garuantee this will work, but the Exchange admin might have Outlook Mobil Access, OMA, turned on as well. It's stripped down WAP like access to your mailbox.
You posted that you can use this to get to OWA:
https://mail.www.xxx.yyy.zzz./exchange/
Try this to get to OMA:
https://mail.www.xxx.yyy.zzz/OMA/
Might or might not work depending on if it's disabled.