None of this would be a problem if DL had strictly enforced its very liberal carry-on rules on the earlier boarding pax. As an "elite" OP learned a valuable lesson in what happens to those people in Group X all the time.

As to the gate check, arguing with FA's/GA's is pointless and a good way to get yourself left behind. But, one thing I do not do is leave the bag without having a chance to examine the tag. If it's written wrong or has the wrong flight #, make them fix it. That may annoy the GA/FA/ramper, but they know they are in the wrong.