This is really difficult, and you are very understanding of the pressures your SS is under, but your baby has to be your priority.
My brother was an awful bully, and excuesed as he was jealous, couldn't cope without having all my mums attention. So he got more attention, but was still mean to me. We have no relationship at all now, as he grew up to be a nasty entitled man.
Your SS could end up the same way - he needs boundaries, and even if it's only 2 days a fortnight in your house, you need to apply them. No hitting, no bullying, and not demanding to be the centre of attention all the time. He needs new consequences as sending him to his room isn't working.
While he may not be able to do much damage to his older siblings, they need to feel safe and comfortable too, and it does sound as if everyone is expected to pandeto the 6 year old.
I totally with everything you say about him needing boundeting, suggesting Cubscetc - you can still sign him up to clubs, he'll go every second week, which can't be that unusual. It will give him some structure, and give his older siblings a break from him.
I know you don't want to put a camera in, but I think it's a good idea. You could get a nanny cam in a teddy which can just sit on the floor by the baby. You might be very happy to evidence that it's your SS harming your baby, not you, not your husband and not the other SCs. Also if you have evidence he can't deny, so you can have a proper chat about why he's doing it, why it's so unkind etc.
I haven't seen my brother in about 10 years, but I do wonder if we'd have had an adult sibling link if he had been disciplined as a child, and if his bullying was treated seriously and stopped.