jerry90210, you're asking for certainty in an uncertain world. Even if you would only be forced to check a bag once in a hundred -- or a thousand -- times, your very next flight might be that time, so you need to have some type of Plan B should it happen to you.

If you go to AA's baggage page, you should find the allowable dimensions for an under-seat "personal" item; but from your description, I doubt that your messenger bag would fit.

As noted by Cledaybuck in Post #67 64, there is a free way for you to get Boarding Group 6 on an AA Basic Economy ticket: just sign up for the AAdvantage program (it costs you nothing), and include your AAdvantage number whenever you book Basic Economy on AA. Boarding Group 6 should reduce -- but not eliminate -- the risk that you would be forced to check your messenger bag. That's probably the best you can do when flying AA if you're not willing or able to pay extra for things like Priority Boarding.