Ok right ummmmmmmmmmmmmmmmm.............................I had Sasa and Misa and then got the 2 birmans and at one point Ducha was attacking the other two, going for the neck.
I spoke to Wizz and she thought I should rehome the birmans as did peeps on CC at the time but like you I had grown to love the terrible two and didnt want to rehome them and the current situation is that the two pairs tolerate each other most of the time. Misa hissses at Franta when Franta gets above his station and the birmans have taken over up stairs.
This means that Misa is scared to go up stairs cos the birmans will chase him back down.
Part of all of this is temperament of the birmans and aslo probably, their age but they dont do the right things in cat language and Misa and Sasa dont understand them. Franta is nearly deaf and he will go and sit and stare at Sasa cos he likes her and he will do a sweet little meow cos I think he wants to be friends but this scares Sasa and she runs away. He also wants to be friends with Misa but they get their communication lines twisted and its never gonna happen cos Misa would like to go up stairs again and the birmans wont let him. Also Misa and Sasa love each other awwwwwwwwwwwwwwwww
So apart from some hissing and a bit of chasing and an occasional paw raised they all live together. I could never rehome the birmans and they dont deserve it but I am sure that the other two would love to see the back of them............sigh, and if I had a crystal ball I would not have taken the birmans.
However we are 4 plus me and it works, they make it work in their own little way and I think that Ralph and Cleo will too.
They may not think each are the cats whiskers but I think you need to let them mix now and get their tiffs out of the way and they will find their own way to deal with each other. If the tiffs become bloody fights then that will not do and it wont work but a chase here and a hiss there should be OK.
My thought on Ralph and the entire Tom is that Ralph was being submissive cos he knew that the Tom could do him damage and he didnt want that.