There are plenty of convenient places to store your luggage in Denver, from downtown to Lincoln street to Capitol Hill and Commons park. The cost is just US$6 per day, and check in time is just 3 minutes. So basically, in the same time it took to make that instant cup of Ramen before rushing to the airport, you can be in and out the door with no luggage to weigh you down.
For longer term storage, there are many self storage units around the metro area. Not cheap, but then neither is paying extra baggage fees and lugging around extra stuff not needed for another leg of your trip, as it sounds like Terry might be doing. For example, I found "Downtown Denver Self Storage" with units starting at $45 a month. http://www.downtowndenverstorage.com/
Just so you know I have tried to call and email and left multiple messages trying to find some middle-ground and give him an opportunity to make amends as I know how determinantal negative online reviews can be for a business but they have not returned a single call or email and know that we are back in FL and she has lost/had stolen many, many expensive and sentimental things we have no choice but to share our story so that know on hopefully ends up having a similar experience.