Amazing advice, as usual, but something has just occurred to me.
This may be cynical to the extreme, but I have no faith whatsoever in your H. Notice how now for a week and a half he has been calling you more often/keeping you sweet right after the weekend when you asked him to sign the paper confirming your financial agreements. He is not stupid, he must have assumed you needed it to show to the solicitor. If it is plain to see for strangers on the internet, it would be plain to see for a person who has been with you for the last 27 years. So, in order to distract you from moving on/seeking legal advice/thinking about yourself, he all of a sudden comes over all loving and caring and talks to you about BB, which is a) bonding for the two of you and takes up a lot of your (and this thread's) head space and b) actually completely irrelevant to your life.
You never did seek legal advice this week, did you? I am not saying this to make you feel bad, it is your life and your choices, but if you presume he is cynically playing you to buy more time, then you can certainly see that his plan is working. He'd rather you occupied yourself with petty drama of BB's alleged paranoias than with constructive plans for your future without him.
This may be harsh, but I heard married men talk about their wives when they are splitting up with them/cheating on them. It is not pretty. What makes you think your H is different, when in fact he had a textbook affair? In order to justify infidelity, men like that will paint their life-long partners in the most horrible way imaginable. As WWIFL said, BB did not develop this hatred of you all by herself. Please, for your own sake, assume the worst.
Also, about time he started to accept some responsibility. He 'can't stop himself' from talking to you about BB? Just like he couldn't stop himself from sleeping with her, presumably? An average 7 year old has more self control. He is a grown man with a responsible job, he does things for a reason and not because he has no control over them! And the reason why he is not telling you what those motives are, is because they are ugly. When he says: 'I love you like I always did I can't seem to stop myself from talking to you about BB/work etc.' He actually means: 'I need to speak to you to keep tabs on your emotional attachment to me and distract you from moving on and seeking legal advice in good time, while I build a new life with someone I prefer.' I think he must have an ego the size of a house.
Feel free to tell me to fuck off if I overstepped the mark, I realise that your H's behaviour makes me very angry.
I really wish you all the best and have a lot of admiration for you, despite the angry ramble.