There's two issues:
1) I wish AA's communication was better across the board. It is definitely bad that one source will show one departure time and another source will show yet a different one. This is definitely a problem with AA. It sounds like they did try to reaccommodate you without charging you extra so at least there is that.
2) However, you did have at least one thing saying the flight was still on time plus it is always best to go ahead to the airport at the original departure time, in case they are able to swap planes, crews, etc (advice might be different at a one gate airport, but a large airport like LGA not so much). Also, with LGA traffic issues the way they are, it's probably best to allow extra time to get there anyways.
So I think I would probably write in and complain about the differences in communications of delays vs on time. You might get some miles or a small voucher as a customer service gesture, but I would not expect them to cover the ticket on DL or the baggage fees you paid to DL.