I think what you want to say to the ticket counter agent (usually them, not a gate agent) is something along the lines of "can I rule 120 this XYZ ticket and fly on northwest instead of XYZ" ?

Perhaps rule 120 isn't the correct rule in all situations, but they'll get the idea of what you want to do - fly their airline on another airline's ticket.

I don't think I ever did this at the front end of a trip. Will an airline take a not-full-fare ticket from some other airline and give you both outbound and return tickets? I can see the "any money beats no money" aspect on taking someone else's ticket for a plane about to go out with empty seats. It is harder to understand taking that same ticket and issuing a today and a "some day in the future" ticket...