Alison
You might like to try "The Orange Maid of Sligo" which is basically an Orange "aisling". Dominic Behan seems to have nicked the tune for "Avondale"!
Also the version of "My Irish Molly" on which "The sash " was based is worth singing.
The point,of course, is to emphasise how inter-twined the two traditions were,musically and, indeed,poetically.
Regards