I'll stay out of your way and let BBS continue to advise you. He's a very sharp guy and very giving of his time to newcomers.
One thing I will observe (as I am sure BBS will confirm) is that the "change" part doesn't affect your score (as in four years plus change). All that matters from a scoring perspective is the integer part of the number. Thus, 4.1 has precisely the same effect on your score as 4.9.
But where it does matter is in the impact of adding an account. Thus if your AAoA is currently 4.1, then adding a new account would likely lower you to 3.x, which likely would affect your score. On the other hand, even if it took you to 3.8, it would only take you a few months after that to cross back over 4.0.
People conjecture that an AAoA of 4.0 is a breakpoint where FICO gives you some extra scoring points.
But the thing is, if you first fix your CC balances, that will improve your score a good bit. Then, once your score is as high as we can get it, you add the 4th 0% card, for its help with the wheelchair at no interest. Suppose the 4th card then takes you to an AAoA of under 4.0. Who cares? Because during the following 8-11 months you are not applying for more credit. During that period you are working on paying off the card and allowing your accounts to age. By the time you actually care what your scores are again, your AAoA will be well over 4.0 again.
CGID is on point with his post above.
I wouldn't worry too much about the drop from an AAoA of 4 years to 3 years. The inquiry and "new account" could just as easily result in a score reduction equal to the AAoA reduction, but those factors will fade away within 4-6 months. As CGID mentioned, take a look at the decimal portion of the AAoA change, as it will let you know when you will cross back scross the 4 year AAoA threshold. If you're sitting at a high 4.something right now, it could only be a few months that your AAoA drops to 3. If you're in the low 4's, it could be a bit longer. If you aren't planning on applying for additional credit though, there's no sweat in losing 10-20 points for 6 months.