It seems to be a problem MS Office sometimes has with various software. I'm guessing anything that monitors the clipboard may cause problems, and it probably monitors the clipboard as well and does not retry if the clipboard is busy.
How to Fix Copy and Paste Problems Associated with Microsoft Office has some things to try, and also mentions potential conflicts with Remote Desktop, Skype, Internet Explorer, and Visual Studio (all from Microsoft themselves), as well as Acrobat and some other things.
Cannot open Clipboard is about Excel but may still apply. People in there have various solutions, including changing the default printer driver to the XPS one (seems strange, but helped several people who had HP printers), and clearing temp space, as well as disabling add-ins which you've already tried.
Clearing the clipboard also seems to help some people, although it is unclear why. (Perhaps some of the Office apps can't put data on the clipboard if it currently has non-test/bitmap data from another app?)
In terms of things Opus could do differently, we could provide an option to disable our clipboard monitor entirely, but it would also break some key functionality (e.g. ghosting files when you cut them, and updating the Cut/Copy/Paste menu items), so it might be useful for diagnostics but probably wouldn't be something you would want all the time. We could also try using the basic clipboard API instead of the OLE one, but I'd have to look into that more, and it could be unrelated.
Given there's no direct interaction between Opus and Office, and Office seems to have similar problems with a lot of software, and is also where the problem is occurring (and it's not happening in other software), I'm leaning toward this being something Office is doing wrong, but obviously that does not help you solve it much, and Microsoft are unlikely to support you if you ask them for help.
If you try the suggestions in those linked threads and find they still don't help, we can look at making a special build of Opus that disables some of the clipboard functionality to test some theories. If something helps them we might be able to add a troubleshooting option to allow it to be changed in normal releases, possibly at the cost of breaking certain functionality. (Please also link your account for us to do this.)