I'm sorry you're in such a tough spot. You're on the right track, it's just hard stuff. You are right to attempt what we call "partial validation," where you're validating his feelings but not invalid "facts." You're right that apologizing for things you didn't do because that validates the invalid.
It sounds like he's picked up on what you're doing, and ironically feels invalidated, as if you've called his facts "just feelings." Don't get discouraged, you're still on the right track. You might try the shorter sentence, "I'm sorry you feel unsupported," while making really good eye contact, and facing him with a soft and sincere voice, then follow quickly with something else, maybe say you'd feel upset in a similar situation, etc. The shorter sentence may give him a smaller target to disagree with.
Another tool to add to your toolkit when you're stuck and there seems to be nothing you can say, is to say, "Thank you for sharing that with me. What you've said is really important to me. I'd like to take some time to carefully think about it. Can we talk about it this evening?" (or tomorrow, etc.)
When things are calm, try to talk to him about what might make him feel more supported. You might ask him if he remembers feeling supported by you (he'd need to be in a decent mood, otherwise the answer is likely to be "never."

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Do you have any ideas about what set off today's incident?
RC