Thank you for your helpful answers!
Interesting idea to go for E minor. With a bit of adhesive putty,
a tune suggested itself. (How out of tune is this still? My ears ain't too sharp.)
The E minor option means I should really also partly plug the top two holes, to get C and D instead of C# and D#. The downside with plugging holes seems that you give up some tones that might otherwise be available through half-holing (as far as the instrument and my poor skills allow).
Supposing I'd want to go the E major way anyway: how might adjusting that one hole affect the tuning of the higher tones, as Michael writes? MTGuru - was this an issue when you fixed the Chinese whistle?
I have two more (larger) frulas. One looks great in black and copper, but produces hardly any sound :-/ The other looks plain, sounds
clean in both octaves, but seems tuned inaccurately and off the A440 pitch standard. As Michael wrote, it's got uniform hole sizes and distances. That is also the case for the flute I am trying to 'mod', but it just happens to end up a bit more closely in tune (except for that G#)... and it looks cool, and I'm so fond of it that I'd love to 'breathe life into it' :^)