I would not make this change at TGW. Instead, try this:

1. Your bag will be checked through from TGW-DCA (presuming one ticket).
2. Post CBP at MIA, make a judgment call. If making the earlier DCA flight is out of the question, forget it and drop your bag. On the other hand, if you are in good time or the DCA flight is delayed, ask AA to make the change and have them retag the bag to the earlier flight. Don't use jargon such as SDC, simply ask whether they can get you on the earlier flight. Sometimes you will be quoted some figure and you may make a judgment call. Sometimes, you will simply be handed a new BP.