Here are two for comparison - RR & PSA. I recall Eddy said something about those signed "Gratefully" - maybe he will chime on. I know her signature 20 years after this..
There was a talented secretarial before Betty Barker I'd want to rule out. Her letters from this period show 2 different solutions or styles to the "w" and "f" IIRC so I'd start there
There are (small) images of both at "It It Real?" From what I saw there and in the letters the OP may be good. Eddy will know more. I know her after 1960.