I have in my hand a 'Cord from the same year as the OP's Rolleiflex-- probably a IIb. Sort of hard to tell as the various lists of serial numbers and corresponding descriptions don't always match up too well (#751xxx). It needs a trip to the cleaners as the slower speeds are gummed up. Otherwise it is nice and clean with a cute little Zeiss Triotar 75mm/3.5 taking lens (bayonet filter mount).
I just got back two 'Cords from the Hippy Era (late '60's to early 70's -- Vb, type 2) that I had sent off to Classic Camera Repair up in Portland for CLA -- they are now in the hands of our students (I check them out for 3 to 4 days at a time). If I get the 1938 camera CLA'd, I don't know if I will put it out for student use. The Triotar was not suppose to be all that sharp in the corners, but nice for portraits. But at its age, perhaps it would be better not to be in the hands of students.
Can't say the I look upon cameras as having genders -- I tend to say "it". Perhaps I would treat them better if I looked at them as being ladies.
Vaughn