Well, things worked out a little bit different than anticipated.

The flight DFW-MAD AA36 scheduled to leave 5.30pm did not leave until 7:05pm due to mechanical, leaving basically 3 a 5 minutes connection time in Madrid. The real annoying thing was that they announced a 15min delay in boarding 6 times (!) consecutively, without being specific.

If I'd miss the connection I would have a10-12 hour wait in MAD, and end up having a second overnight trip. GA was not very helpful at all. Called AA desk and there was a backup via LHR.

In the end I decided to chance it, and lo and behold, Lady Luck had her hand in it, since the connecting flight was right on the opposite gate in the same terminal 4S. A GA, not sure if it was AA or LY was waiting for us in Madrid and whisked us through a "magic door" right into the departure area without having to face the mandatory Swine-Flu check or other security checks. ( All passengers are required to fill out forms with seat location and phone numbers, even transit passengers).

So all worked out in the end, except I still have no clue what the normal procedure is. As a connecting airport it seems by far preferable to LHR, as long as the connecting flight leaves from the same terminal, which all Iberia flights do.
I may consider it for future South European connections.

Thanks for the advice.