singing the song naturally with my own voice/accent, in accordance with what I've got it writ on the page (or cobbled from other singers versions), while simultaniously heeding the specific peculiarities of dialect (rather than 'accent' as such)

Yes, it's a tough one. When I've sung Jenny's Complaint I've sung it in more or less standard English, because if I attempted the dialect it's written in I'd sound ridiculous. But the last verse begins

What can I dee? I naught can dee
But pine and whinge about him

...and then rhymes 'dee' with 'me', so I can't switch it to 'do'. Now, if I sang "What can I dee?" in my own accent it would sound stupid - as if I'd suddenly decided 'do' was pronounced 'dee' off my own bat. But if I suddenly dropped into my half-formed idea of what a Geordie accent should sound like -

THINKS: Why aye Newkie broon howay the lads
SINGS: What can I dee
THINKS:bonnie lad...

it would sound even worse. So I just try and make the 'dee' sound Geordie-ish and lean a bit on the vowels either side -
What can ah dee? Ah naught can dee
- and beat it back to the safety of my own accent as quickly as I can.

In next week's folk accent masterclass: Ee Bah Gum Is It Me Or Is It Getting A Bit Chilly?