From what I can understand about your situation, you have a bitch, you know the names of sire and dam but as you weren't given the paperwork for your bitch, you don't know which of the 4 bitches in her litter she is. Chances are none of them was registered with the KC for some reason, although it sounds as if they were. It used to be in the past, that with the information, reg. numbers etc of the parents, an owner as opposed to the breeder, could register an individual dog.
If 'only one of the 4 HASN'T had the transfer registered', then surely the one left is your bitch? But I suppose if one of the 3 who were transferred, ended up in Rescue, then she could be one of the 3!!! Even so, you'd have to have the original Registration paper signed by the breeder/initial new owner, to be able to register a transfer into your name?
Hopefully somebody here will recognise the Creccamarch affix and so that breeder, who may have enough information about what's been going on with the bitch you now have, in the past 5 years, can help you.
I suppose being able to, presumably eliminate the one who didn't have a Transfer registered, means she's one of 3, not 4!!