I've seen Eilidh (which is my fav as my dd's name) Ailidh, Aileidh, Ailie, Aili, Ailee, Aillidh, in my line of work. But definitely prefer the traditional spelling. A wee stall in York's shambles had her name there.
Lovley name. Keep the proper spelling particularly as you are in Scotland. It's not a popular name but there are enough out there so most Scots wouldn't have issue with the spelling - Ceilidh without the C. I would have though trying to make the spelling simpler will mean your daughter spends more time correcting the spelling to the people who spell it the traditional way then she would have teaching the people who don't know how to spell it. It's one of those names that in my opinion you would know if you didn't know how to spelling, ask, and that would be the end of it rather than altering the spelling and her getting Eilidh anyway.
Lovely. Was going to use it dd but decided against because we are in England and spelling difficult. Then when pregnant with dc2 decided sod the spelling, lets use it! But dc2 turned out to be ds so never got to use it!