I didnt really read the whole thread....but that is tough one. I am not looking forward to dealing with it in 17 years.
I can compare the two different dynamics though. My wifes mother and father were very strict about that (like how you are proposing) and she just did things anyway behind her parents back.
In contrast I dated a girl for a long long time and when we were 17 or 18 I was ALWAYS spending the night at her parents place. I had a good relationship with her parents and I think it showed her parents really trusted her. Yeah we banged all the time there, but her parents never bothered to 'check in' or anything. Certainly could have.
What I am saying is, I dont think it is bad to allow someone else to crash at your place so long as you set expectations. Otherwise, she is going to be crashing over at her friend "Jennifer"s house and you wont be none the wiser....Well. I am sure parents are always skeptical about if most kids actually do what they say they will or wont, but if they are HOME, regardless of who might be staying over, id call that a win.