when i start to feel that oh so familiar frustration at not being heard, i use the STAR method.
stop
think
assess
react
i use to draw a star on my hand to remind me. it really helps.
for example, when the blaming, illogical nonsense began, i would recognize it, look at the star on my hand, say something like "excuse me for a minute" and take a walk around the block or step outside. then i would think "what's actually going on here?" ...sometimes that would take a few minutes to determine...maybe take a stroll down by the water and unconfuse myself...
after i began to practice this, the action to take would become clear. at first, i felt like i had to rush, because obviously, the other person was back there waiting on me. then, i gave myself the freedom to take as much time as i needed to determine my response. i actually began to enjoy these little walks, thinking "oh, this is so much better than reacting...breathe in the new, exhale the old, naive...oh look, the moon's rising....now, what was it he was harping on about.?..doesn't really matter does it, naive....can't reason with a drunk...oh, there's the baby swans!"
in most cases, my action was to return to the person and calmly say "i have some other things i need to do now. let's talk about that another time." and then left.