@Michelle2914 While I know it seems unfair, I imagine you can understand the hesitancy. Most 18 year olds, while they may not be irresponsible partiers, also tend to not know how to look after a home. That's not a put-down, it's a natural consequence of being 18 years old. So you and your friends could easily do things like cause damages to furnishings, simply through inattention or not understanding what can cause permanent damage. 18 year olds do things like fire up the washing machine on full load to wash one pair of jeans they want to wear that night. Take 1 hour showers, strew glitter around.
I raised 3 daughters, so I speak from experience. They certainly weren't destructive, and I used to let them have parties at our house because their friends were nice kids and my daughters always cleaned up afterwards. But still, some of their friends would do thoughtless things, like one who mindlessly carved his initials into our coffee table. And a couple of times word got out that there was a party, and all these random kids my daughters knew from school, but who weren't really friends, would show up and things got out of hand.
It's actually a really good idea for you to book a couple places for a few nights on your own or with just one friend to build up a few reviews. Look for studio apartments attached to a host's home, so they won't be worried, like a host of an entire place might be. It would certainly give hosts more confidence in renting to you if you had a couple of excellent reviews.
For your grad gathering, you might try to look for places where the host lives onsite- like a place in the countryside where the host lives in another dwelling on the property. Hosts of those situations are more likely to be open to giving you a chance, because guests can't get away with bad behavior, as the host is nearby and can see if things are getting out of hand.
I'm surprised that hosts told you " Requiring that a parent, with reviews, book (none of our parents utilize Airbnb, this just feels super unfair to us)", because that is actually totally against Airbnb policy- it would be a third party booking, which are not allowed. The person who books has to be among the group that is staying.
Another thing I would suggest is that you update your profile blurb. Your profile write up is supposed to be a little mini-bio, not a description of what you are trying to rent. It should be about you- your interests, your schooling, part time jobs you have or have had, volunteer work you might do, your general life attitude. In other words, giving hosts a sense of the kind of person they are dealing with.
But I have to tell you that this is a relatively recent phenomenon, where teenagers want to rent a house to celebrate something. Even back when my daughters, who are grown now, were teenagers, if they wanted to do something like that, they all went camping somewhere. Which is something you might consider as an alternative- it can be a ton of fun. You can bring camp stoves, folding tables and chairs, good tents and real foamies, blankets and pillows, games and other amusements, plenty of food, and enjoy yourselves without having to try to convince anyone that you'll be responsible.