"or they sing in an accent that's impossible to understand."

Yeah - I've tried in a couple of the songs I sing that contain Scots dialect (Alison Gross & The Great Selkie of Sule Skerrie), to stick to my own accent throughout, while anglicising *some* of the less easily interpreted dialect words and retaining others which can readily be understood in context of the verse. That approach strikes a happy medium for me, though it might not be to all tastes. With AGross as I sung it in a session - I gave the audience an easily remembered anglisiced chorus - while singing the dialect myself (as I find the words nicer to sing that way).

I expect that's how I'll treat longer ballads with dialect too, though no doubt a brief pre-amble is a good idea so people can hold onto the plot if some dialect phrases are not rendered clear from the context.