Hopefully the mods will come along and merge this into one of the other threads on the same topic.
Bottom line is that as AA makes plain, there are restrictions on certain items on certain aircraft. This particularly applies to "rolling luggage" which are forbidden by a number of the Express carriers.
As always, the issue has nothing to do with whether the bag fits, whether you are in F (even paid F), whether you are CK or D(irt), or otherwise VS (Very Special). It also has nothing to do with whether some other FA on some other flight did not enforce the rule.
One can argue policy all one wants, but arguing policy with the FA is fruitless. There are two approaches. Gate check your bag and live with it or politely explain your time crunch issue and hope for an exception and graciously accept the answer without back talk if it is "no".
W&B is not likely the answer here, it is more likely simple customer dissatisfaction. OH space is a zero-sum game. OP gets to stash the steamer trunk sideways, taking up the space which three compliant bags would take and there are now 3 passengers who have to gate check vs. just OP.
Hopefully the F-tag system works and you get your gate check ahead of the others.
Alternatively, maybe a lot of people buy BE fares and the OH's are empty and the "rolling luggage" distinction goes away.