how to enter product key for publisher 2013

I'll give you my reason:

I have 3 copies of MS Office 2013.

When I go to office.com/setup and enter my newest key it brings me to the download site, where two products are listed (neither of which show which copy of office is which).

To determine which key goes with which download I go to the advanced options and reveal my key.

However, neither are my newest key, so I cannot simply run either installer and have my new key automatically associated.

So, I install another one with the wrong key, but now must change that key in order to activate my product.

I hope this helps contextualize my issue (and I think the other issues in the forum).

So, is there a way to change the product key? I've tried the command line option with no success.

Thank you.

I appreciate the constructive help, but as someone who is searching google for "change office 2013 product key" coming to a forum where the responses ALSO include "Why do you need to change the Product Key" aren't helpful, either. It would be nice if forums would just answer the questions asked so that they could be a resource to people in the future.

I bet we won't receive a proper answer to  this question by Microsoft, but this is real question, and I will try anyways, even though I know it's futile. 

I am the lone support technician at our mid sized company, and can ill afford to spend hours on such a simple operation as changing the activation key for a Office 2013 install, especially when this would only took a minute or two with past versions of Office.

Please tell me why Microsoft has chosen to make such a simple task as entering a new activation key for Office 2013 so difficult and a waste of time, for anyone who has already paid the high cost of Office?