While I am also fond of Michael as a girls name, I have to ask. Are you going to spell it with 2 i's, or was that a typo? If you are going for the unusual spelling, may I ask why? If I may... then why?
The examples of people who have had that name, and inspired your choice, seem to have had the more common spelling, so I'm intrigued.
The two "i's" were not a typo...I wondered if anyone would notice. LOL
We thought about just plain Michael...and also about Michal...and then about Mychal...and Mychael...and, and, and. Then one day I was playing around and I typed in Miichael--and it just clicked. I don't know why. So I showed it to Mr. H and he got this amazed look on his face and said, "that's it! That's how it should be spelled!" So here we are...with a Miichael--with two i's. LOL
I'm not a fan of really creative spelling (which is why we were having trouble with the name--I didn't like all the y's) so I don't know why this spelling clicked for both of us.
I know. Weird. LOL
I just hope the teacher doesn't think she has two illiterate, low class parents. 
Okay, I have one of these intentionally misspelled names-in a remarkably similar way, actually. Let me tell you, that is exactly what almost everyone thinks. Every teacher I've ever had has asked me if my parents misspelled my name by accident. Every friend, every admin person, everyone.
You should really not do this. I have spent hours at the DMV, and even more time in corporate HR offices because new job called old job for a reference, someone didn't notice the odd spelling, and new job was told that "no one by that name ever worked here," because I didn't come up on the computer. My high school transcripts didn't get matched up with my application when I applied to college. Medical offices can never find my paperwork. I have had to get reissued passports twice. The insurance company, the gas company, the bank-I log more hours on hold getting this fixed than anyone I know (and that isn't a figure of speech). As a little kid, every award I got had my name written in fancy calligraphy, and a second letter squished in with a Bic pen at the last minute, if anyone noticed at all.
It is not because my name is unusual, but because the spelling, like yours, looks like a typo. You can mention it and spell it out, and it will still get entered wrong. If you have an unusual name, people will take note but even you assumed in your original post that people might not notice the "ii."
My parents took what could have been a perfectly nice name, and made it a life-long pain. If it was unusual because it was ethnic or familial or tradition, I might have a reason to be proud, but it is just misspelled. I consider it a total lapse of judgement on their part. After a few years of seeing how much trouble it is, they agreed. Actually, for my birthday this year, they are paying the fees for me to legally change it to the correct spelling.
I can't tell from your second post if the child has already been named, but I highly recommend that you reconsider if it hasn't. I know this was blunt, but I'm not sure you've considered how much trouble this is going to cause. You add the "LOL"s to your post, but are you still going to think it's funny, when you explain for the gazillionth time that it's "ii" and then, have to listen to questions about who misspelled it, you or the hospital-and even after all that, the person still spells it wrong?
Go with the "y" version, if you must, but is an odd spelling really that important? Even you admit to not liking them. Michael still wouldn't be that common for a girl, so you'll have your unusual-factor that way. Don't you think that it would be nicer for your child to be able to say, "my name is Michael," and generally have is spelled right, as opposed to my usual conversation, which takes at least five times as long and ends with my name misspelled anyway.
