I don't think Harry would brag about that because it was a horrible experience. And about the rest...I think soulgazes are dangerous. You live all your life with the memory of something potentially horrible. And the Senior Council knows things about Harry (starborn, at the very least) that made them mistrust him. I do not think they want to risk soulgazing Harry. But perhaps is also because if they see nothing wrong and had to release Harry of any charge, Harry would know them very well, and that could be dangerous for them too. I mean, good or evil, Harry is dangerous and not someone to mess with, and he is now bound to obey Mab's word and (from the Council POV) perhaps even in a thrall by a white vampire or two. You don't want a person in that condition to know you intimately. At least, that is my take on the topic.