Oh my, delicate. You may well be gilding the lily. You're entering the no-man's-land of politically correct euphemisms. There's no telling at all whether what you come up with will satisfy all parties. Keep in mind that the phrase "mentally ill" itself was introduced as a polite replacement for "lunatics" and "crazies" and other such insulting words. The phrase "mentally ill" was deemed to be quite a step upwards from its predecessors.

Has anyone invented anything better? I don't think so. The "phenomenologically challenged"? Dubious. Very dubious. My suggestion would be that if your project is undergraduate that you pay no attention to such highfalutin' concerns and simply say "mentally ill." If, however, you're working on your master's or Ph.D., you might want to sneak a look at your professor's prior publications and use whatever term they may have used most recently.

It's really a "no-win" situation, delicate. You'll catch flak regardless. There will never, ever be a term or phrase that makes everyone happy. Might as well stick with what makes the person grading you happy. Machiavellianism.