IF the original flights still operate
AND
IF the connections still work

I would accept nothing less than traveling on the original flights booked.

Airlines don't just offloads mileage redeemers from flights for any reason. It usually happens when flight schedules change and the rebooking is done for all passengers, not just those on mileage tickets.

Airlines sometimes try to save money by only rebooking the passengers on flights that still have the original booking classes (mileage or paid) available. However, in my experience, if the passenger insists, they always will override this and rebook the passenger(s) on flights as similar to the original ones as possible.

IF there has not been any schedule change and passengers are simply being changed to other flights at the airlines whim, I would complain to the DOT.

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FYI - Bumps usually refer to day of flight. Around 50% of flights are overbooked; only a small fraction of these bump people because usually 5%-20% of the passengers don't show up. In those rarer cases that too many people show up, the airline will ask for bump volunteers. These people receive compensation to take later flights.

Occasionally not enough people will volunteer for the bump in exchange for compensation. So the airline will have to involuntarily bump someone - IDB (Involuntary Denied Boarding). The DOT requires airlines to provide specified minimum levels of compensation in these circumstances.

I am not positive if IDB rules would apply here, but if they do AA owes you cash if you insist. The problem might be that the DOT rules a % of fare paid, and you paid with miles, not $....