I was always under the impression that Harold Hill sang "The Sadder but Wiser Girl" as a way to deflect overtones that he was falling for the prim and proper librarian. That in fact, Marian Paroo wass the antithesis of the "Sadder but Wiser Girl".
Also, the ages of the Paroos are a bit vague. Nowhere is it stated that Mrs. Paroo is 50-60 years old, so it is conceivable that she could be in her mid to late 40's. That would put Marian being between 21 - 25 and her mother's age at around 20 - 25 when she was born. If Mrs. Paroo is ~45, Marian ~25, and Winthrop ~10 -- that would put Mrs. Paroo's age at around 35 when he was born. Not young -- but not too old by any means -- even for the turn of the century. I think the better explanation is that Winthrop was an "accident."
(Of course, to give your side some credence -- a lot of theatre groups do have a habit of casting Mrs. Paroo a little too old which WOULD make Winthrop's origin come into question)
"You pile up enough tomorrows, and you'll find you are left with nothing but a lot of empty yesterdays. I don't know about you, but I'd like to make today worth remembering." --Harold Hill from The Music Man