FM said: One of the triggers is an old one: H was returning from his second night shift in a row...that's always been a "danger zone" for conflict.
But for some reason he's not sticking to what I assume has been a self-imposed "code of conduct". He is falling into ruts -- like making mean comments and starting arguments.
You answered your own question. It's stress, anxiety, depression plus sleep deprivation. That's why he's not sticking to his code of conduct. I would plan to be away from him ALWAYS for now if possible after second night shifts in a row.
I would look to be in another part of the house during child exchange when he will be in a predictably fatigued mood from a second night shift in a row. Otherwise he will blame it on you and he may not be in a space to control himself for awhile. Just a thought. My H, who has some kind of depression and anxiety issue going on now, told me recently that he feels predictably worse at certain times of the day. He claims that that influences when he is willing to even attempt to see me (and maybe anyone?). I don't know if it is because of fatigue or because he feels he will not be able to be civil because of his own mood. Just something to consider. Your H may need you not to provide the opportunity for him to get into it with you for a few months to realize that he is looking to start something on his own even if you're not there to start it with.
Some of what LR calls attempts to start "bun fights" aren't testing. They're meltdown. I'm not suggesting to make a practice of walking on eggshells for life. But a cooling of the jets has to happen, and he may not be able to make it happen totally right now, so choose your disputes wisely, I guess.