Originally Posted by
Often1
Given that OP has an inflexible schedule, there really isn't much to be done other than perhaps travel with a small carry-on which he won't have to gate check and thus not have to wait around for valet luggage.
AA 6037 is an E75 (at least currently), so rollaboards can go on board and there's no valet checking. But I would be sure to be on board as early as possible in TUS to ensure that OP gets overhead bin space, which can be tight on E75s.