But it depends a whole lot on what we mean by 'morality'.

What I mean by "morality" is the part of normativity ("what you really ought, all things considered, to do") that has to do with values (as opposed to rationality).

I agree that it's going to take a lot of work to fully clarify our concepts. I might be able to assign a less remote probability to 'morality turns out to be impossible to carefully reason with' if you could give an example of a similarly complex human discourse that turned out in the past to be 'impossible to carefully reason with'.

In general, I'm not sure how to show a negative like "it's impossible to reason carefully about subject X", so the best I can do is exhibit some subject that people don't know how to reason carefully about and intuitively seems like it may be impossible to reason carefully about. Take the question, "Which sets really exist?" (Do large cardinals exist, for example?) Is this a convincing example to you of another subject that may be impossible to reason carefully about?