Giving this thing further condideration...

Having got rid of the pointless rape and given Lady Jean a more proactive role in the proceedings (it now goes:

So SHE took HIM by the middle so sma'
An she's danced him roond the green
And she laughed and she sang til the deed it was done -
An she bade him dae't again, my luve, she bade him dae't again.

And he said 'Now sin ye hae got your will o' me,
Pray tell to me your name,'
'Oh I am the King's young dochter Jean -
But this night I'll ne'er gang hame, my luve, this night I'll ne'er gang hame)

I've decided there's no way this is cause for any sort of shame at all, much less a double suicide. So after the brother mithers on about wishing his pretty ship had sunk, Lady Jean brushes his concerns aside thus:

'Oh, brother dearest luve, I couldna gie a nit,
Not for God nor for the law;
So come awa wi me in the merry green wood,
Where we'll live as white as snae, my luve,
we'll live as white as snae.'

So they live happily ever after, or for a week or two, until she gets bored with his mithering (& consequent impotence) and runs him through with his sword to return home:

'Oh what's that red that stains your petticoats?
Come tell me, Lady Jean' -
'Oh tis nothing but the glint o' my monthly bloody flow,
That came on yestere'en, my luve,
that came on yestere'en'

End of ballad.