Barbara Allen based on no hard information whatever
Pepys described [Barbara Allen] as "an old Scotch song'

No he didn't.
From this website - Barbara Allen

A diary entry by Samuel Pepys on January 2, 1666 contains the earliest extant reference to the song.[3] In it, he recalls the fun and games at a New Years party:[7]

    ...but above all, my dear Mrs Knipp whom I sang; and in perfect pleasure I was to hear her sing, and especially her little Scotch song of Barbary Allen.

From this, Roud & Bishop have inferred the song was popular at that time. They suggested that it may have been written for stage performance, as Elizabeth Knepp was a professional actress, singer, and dancer.[4]

"her little Scotch song" suggest either something she wrote or something that was written for her.

Excuse me if I place more confidence in Steve Roud's judgement than yours. I might ask him about it next time I see him.