Interesting. In theory if the ticket and the reservation weren't linked correctly, a boarding pass shouldn't have been able to be issued at all (the primary function of the check-in process is to check that the reservation and the ticket properly reconcile to each other). So that may have been part of the confusion.
The gate agent really should have been more helpful, and certainly should have taken a minute to try to see what was going on with your ticket before processing standby passengers. But unfortunately they weren't.
And unfortunately not much more can be done about it at this point. Delta offered you miles or cash, which are their currencies of apology. If those don't help, I'm afraid not much else will. You could write a polite, to-the-point, unemotional reply to their original offer and try to get more, if you want, but that's about it.