Okay, here's a theory...
I know that children were often baptized together rather than individually, and I have a baptism record for three of my grandfather's brothers being baptized on the same day, despite being born a few years apart.
I found a baptism record for a Charlotte Ellen Smith
here. What do we think to the idea that she was born Ellen Smith c1869, but was baptized - perhaps with some of her siblings - and given the name Charlotte in 1876?
That gives us the right name, the right location, and the right parents.