Mihai,
Isn't that exactly what the seller data field is supposed to be used for though?
I'd prefer not to have any of our plumbing (like unique order ID from our database) exposed to the user. Putting our unique ID in the description might confuse the user because they'll see the Google order number and ours. Also that means that every order would have a distinct description. I don't know if that is not ideal at this point, but it just doesn't seem natural.
You suggestion should work, but it just seem ideal. However, if seller data is never going to be exposed on the merchant center, then I guess I have no other choice.