This dynamic is very familiar to me. I've tried various techniques to respond when I am being blamed for something unfairly. I say, 'what do you want to do about that' or 'I can see that really bothers you' or 'I can see you hold me responsible for that' as ways of showing empathy and rejecting responsibility, and they just tend to inflame the situation. The best results I get at the moment are to just end the conversation.
When H brings up the past to blame me for it, I don't point out my changes or his part in where things went wrong. I say 'yes, I think you're right, there are many things I need to change about myself. The one thing I can't change is the past and how that has affected you and our relationship, and I understand you're angry about that,' - that has sometimes calmed the situation but not always.
