OP's situation is an unfortunate series of events, but seems to run contrary to what AA generally does. JonNYC has recently posted AA's internal policy for rebooking in IRROPS and it greatly favors elites with lengthy delays. It is also my impression that AA clearly blocks seats in IRROPS so that it can move stranded pax and that its overbooking algorithm accommodates large-scale IRROPS by recognizing that there may be less availability, but that there will be more no shows.
There are certain things which are new and which do suggest a bit of research before seeking accommodation.
#1 - Flights are full. That is true not only for AA but across the US. Full flights means fewer empty seats available in IRROPS. But, that does not preclude standby and that is the route in large-scale IRROPS. Overbooking flights beyond what can likely be accommodated simply prolongs the misery and is not financially responsible.
#2 - Before speaking with an agent, have the research in hand. Asking for a reroute is rarely a good idea. Always better to have reroutes in hand to propose. When you do that you will more likely get what you seek than waiting for an agent to come up with what you like.
#3 Be flexible. If getting to your destination in a timely manner is more important than your F aisle seat, make a point of saying so.
Finally, remember that one of your options if a flight is cancelled or substantially delayed is a refund of the ticket. It is not always the case that other carriers will be more expensive at the last minute. Bear in mind that AA does not interline with B6 or WN. In the case of DCA-ABQ, there are at least 9 frequencies a day (all with at least one connection). But, AA cannot book them. You can. If you can see positive space on WN, grab it, and cancel AA.
It is always helpful to have a high-end corporate TA with 24/7 backup which can handle IRROPS for you, including making hotel arrangements. But, if you don't have that, a bit of prep in advance can avoid problems downstream.