I am a little late to this thread, but have read it and just wanted to offer my 2 cents.
I've been bitten, with skin broken, twice. Once was breaking up a fight between two 8 month old Dobermans, which was my fault for getting in the way, but I wasn't really thinking of anything other than "get the dogs away from eachother". And the most recent was an Aussie bite because I unintentionally surprised the dog and I guess she wasn't expecting another person to be in her house. I was a little shocked and didn't even want to tell her owner until my hand started to throb and I couldn't exactly hide it, but again, it was provoked. That reaction is one I hope my dogs wouldn't have themselves (to bite when surprised), but I understood it and certainly didn't think ill of the dog.
Those are bites that I can totally understand and don't really fault a dog over. The last one, like I said, I wouldn't tolerate from my dogs very well, but I could understand it and it would be something I'd work on.
I've also had the experience of living with a very unpredictable, unstable dog. He just had no predictability about him at all and would just lunge forward to try and grab somebody. There were warning signs, but no clear triggers. What he was fine with one moment, he was not the next. Thankfully he never made contact because he was managed well in the time we had him, but he sure tried. We adopted this dog, and while they performed some sort of temperament tests on him, they barely had him long enough to really know anything about him. He was put to sleep. A dog like that is NOT a dog I would ever keep or give to anybody else. No matter how much work or time I could/would've put into him, I'd never have trusted him. Too much risk and liability. There are so many stable, non-biting dogs out there... I myself just could not justify keeping a dog like this dog around.
With that said, Bamm does not sound nearly as extreme as the dog I mentioned above. He's pretty happily lived a good life with Amber and has come a long way and made huge progress. But, he certainly appears to have a level of unpredictability about him. A dog shouldn't appear to be nice and comfortable and then freeze and stress and want to bite for no apparent reason. Behviour such as that might be manageable now, but I would be very concerned with having him around a child, and with as much time and energy as a child takes up, I can't imagine trying to balance life as a new mom, with two other dogs, and a segregated dog while giving everybody everything they need. I think I'd worry that if Bamm had to be segregated from the baby that he might become more stressed and frustrated, and thus he might take some steps backward and become more of a bite risk.
I honestly can't say what I'd do in this situation. Amber, Bamm has been with you for so long now and I know how much you love him and how heartbreaking it would be to have to figure out what's going to happen in the future regarding him. He's obviously very well loved, well trained and well managed.
I feel like if I were in this same situation, with a dog like Bamm, I'd probably give some serious thought to having to potentially euthanize. For myself, there is just too much risk involved from the sounds of things. From what has been said about him throughout the years on this forum, I just really do not think I could trust him around a child and it would likely take a lot of management in and around the home to make sure he never had a chance to injure the child. I definitely would not want to see him put into rescue for the reasons Sizzle mentioned, and I feel like rehoming him would not be easy and it'd have to be to just the right person who totally understands what they're taking on. But I know it's way easier to sit here and speculate about a dog that's not mine. This is a tough situation and one I hope to never be in. And I also don't have kids and don't know if I ever will or not at this point, nor do I have a dog I'd consider to be a bite risk toward a child or anybody else... so while I sit here and think, it's really very hard to even suggest what might be best.
With as much time and years and work that you've already put into him though, I'd likely speak to behaviourists first and give him a chance, because it's not as though he's outright aggressive and constantly biting. The bites he has had have not been good, but all in all, it sounds like he gets through most days relatively uneventfully.