Thank you for posting the rules. It seems that four-hour is AA's interpretation of "significant delay." My best option right now seems to be to book the DL flight and use the flight credit for a future ticket.
BTW, what is the difference between a flight cancellation and a schedule change? Strictly speaking my original flight was cancelled and replaced with another. It seems that under the flight cancellation rule I would be entitled to a refund...
If AA has put you on a flight with a different departure time
and a new flight number, I suspect that the DOT would say that your original flight was "cancelled," and that you are entitled to a refund. If the flight number remains the same, then maybe not.