The word "moral" is ambiguous enough that some uses of it are as you make note of, but others, especially among philosophers, are defined as meaning "inescapably practically rational" or "maximally prioritized." Bernard Williams was one philosopher who did object to the "peculiar institution" of "inescapable" moral codes, but so rather than looking at the question as, "Is anything moral?" we can just ask, "Is anything inescapably rational for us to do, or is anything a maximal priority for us to do?"
Or, then, we can ask, "What action would promote the greatest net happiness in actionable circumstances?" or, "What action is categorically imperative?" or, "What action conforms to the principles derivable from the original position?" or, "Which actions express the implicit commitments of reasonable discourse?" (a Habermasian protocol, I think), etc. It is not clearly obvious that these questions admit of only feeling-based answers. Now one might wonder why we "ought" to promote the greatest actionable happiness or comply with categorical imperatives or the principles of abstract social contracts or whatever, just as one can ask, "Why be moral?" in the first place. But again, that will seem to be an inquiry that answers itself by definition: "Why be moral?" can be translated into, "Why do something for which there is a 'why' for doing it?"
In other words, asking why as such itself only has meaning if you intend to act accordingly when provided with answers to "why" questions. Otherwise, you'd be merely displaying, not sincerely asking, why do something.
Alternatively, another abstract definition of "moral" has to do with an imperative that Kant described as "analytic": "Act according to the truth." (Rawls speaks similarly of actions that "express our factual nature" (A Theory of Justice, sec. 40).) The idea is that there are some behaviors such that if we engage in them, this is somehow tantamount to having true or false beliefs thereby. For example, murdering someone in a fit of rage might be interpreted as failing to correctly believe that we have the willpower to constrain feelings of anger. More circularly, murdering someone out of cold spite might be thought of as failing to correctly believe that the victim has the right to not be murdered. It will be objected that the heated example trespasses, in theory, upon the is/ought barrier, whereas the chilling one is, again, circular.
However, at any rate, what can be made, if anything, of moral theories based explicitly on fighting against feelings-based decisions? Are those theories feelings-based nevertheless? If I adopt a moral code that tells me not to ever have sex, no matter the temptations and opportunities that arise, and yet there are no supplementary or even complementary principles in the given code that would explain this prohibition on the basis of my possible feelings about other subjects (e.g. the code does not claim, in the background, that having sex will lead me into Hell), then it is at least fairly debatable whether this prohibition reduces to just a "neurotic" self-command.
