Good Sam Mail Service

I have a box and want to cancel it and put in a change of address, so mail will no longer go there but go to my current address out in NM. I just called to talk to someone about it and was told that it's not possible. That because they are a mail forwarding service, I can't put in a change of address. "Or everyone with the name of Smith would get forwarded to the new address."

I objected, she said it can't be done and said I should contact each person who is mailing me at that address. Well, for reasons I'd rather not go into here, that's not going to work.

Why can't I just drop a change of address card in the mail (out here in NM) and have it go into the postal system so anything addressed to FL goes to my current address? Am I missing something here?

Thanks for any input.