"Until relatively recent times these melodies were strictly unaccompanied" - and I personally think that's a good way to sing them. The standard tuning works pretty well for the dance tunes, the jigs and the reels.
The problem isn't getting the different keys, it's switching around between them at speed. There are those who can do it with the funny tunings, but I've never been able to.
Davey Graham worked out his tunings mainly for playing Arab and Berber music in North Africa. Anyone on the Mudcat go in for playing that? They use bodhrans out there too, they just play them a different way.