So to report back. I upgraded my Yosemite machine direct to Office 2011 SP3. It rebuilt its database when starting and now it connects to both my account and your test account.
To try and determine what exactly fixed it, I upgraded the Mountain Lion machine to SP1 (I had to anyway for SP2). Still didn't work as before. Then I upgraded to just SP2. Again the database rebuild happened. Created the account and it works fine now too.
So it seems for me SP2 or later has fixed the problem. I don't see anything specific in the release notes that indicates it should help, but both machines weren't working, I updated them to SP2 and SP3 and now they do immediately after.
NB: The Mountain Lion machine without even SP1 did work with our previous hosted Exchange service. I didn't have the Yosemite one at the time.