AA is fine but you will actually depart from a remote terminal so that adds more time - you have to take a 15~20 minutes bus ride from T4 to the remote terminal so 2.5 hours is pretty tight for this kind of connection. Ideally you will want 3 hours to connect two separate tickets that departs from a remote terminal.

This is the steps you have to go thru... You can do it in 2 hours if everything goes smoothly but an easily take 3 hours if something slows you down:

1. Walk from NZ2 to TBIT immigration - 10~15 minutes depending on which gate you park.
2. Clear immigration - 30~60 minutes depending on how long is the visitor line. You will need to be photographed and finger printed.
3. Collect luggage - up to 60 minutes. This is the part people always forget... chances are that you still need to wait for your luggage after you clear immigration.
4. Clear customs - 5~20 minutes. Assuming you have nothing to declare, this could take no time at all or 20 minutes depending on the line. NZ2 is probably not one of those flight that gets extra screening at custom but I'm not sure what other flights are arriving around the same time.
5. Walk to T4 - 2 minutes. This is the easiest part of your connection.
6. Check in with AA - 5~30 minutes. You can probably use the self-service kiosk so it takes only a few minutes but you still need to drop off the checked luggage so you have to go to the counter. Lines could be long.
7. Clear TSA - at least 20 minutes. You have to use the regular security line at T4, unless you have elite status with BA or QF.
8. Walk to the T4 bus stop - 5 minutes.
9. Wait for bus and ride to Eagle terminal - up to 20 minutes.