I find this chart for single key flutes
http://www.oldflutes.com/charts/onekey/ gives plenty of things to try out. Several of them, even those that show the key in use, work more or less as described in the comments on my small-holed Burns folkflute. On a large-holed flute many may not work.
Second octave G# with XXO XOX is a good strong note for me but doesn't work on some large holed flutes. A high proportion of the few tunes I need G# for only use it in the second octave. First octave G# XXO XXX can be blown into tune but is very veiled. One or more options for the three second octave notes beyond the normal 'Irish' range works for me - but I need to practice.