Jim,
Okay, I'm hooked. The phrase 'I've lost my love and I care not' I'm sure I've come across in my searches through Roxburghe Ballads but in what I can't remember.
However here is a variant to add to the pile from Greig-Duncan Vol 6 p192 as sung by Margaret Gillespie. It goes to the tune 'O'er the Water to Charlie' the A version as given in Greig-Duncan.

I've lost my love an I keena weel fu
I've lost my love and I carna
For laith would I be jist to lie down an dee
An to sit down an greet would be bairnly.

O plague on the men their so sly an demure
As pawky as diels wi their smilin
As fickle as winter in sunshine an' shower
The hearts o' fair maidens beguiling.

I've lost...as 1
I've lost...as 1
The lossing o' ane's the gainin o twa
Fain wid he come back but he daurna.

Following up the Jean Redpath connection might prove fruitful.