Thanks everyone for the input and feedback. Sorry it took me a while to respond as I did not have time to call AA back till this afternoon.
I’m pleased to report that I got lucky the third time around!

I first used Expertflyer to find “I” availability for a July date (exact same routing as my original flight).
Then I called AA and asked for a ticket change. This time around, they processed it without asking for any additional fare increase. So it sounds like it has nothing to do with carrier surcharges or seasonality (despite what the second agent told me). I think I just lucked out with an agent who knew how to do this properly!

Not very comforting (I would rather have agents who are consistently competent) but I guess lesson to learn here is.. sometimes it’s worth calling again (and again) until you get the right answer!

Thanks again to everyone who shared their expertise and helped me realize it was worth pursuing this further with AA!