Okay, the suggestions Arlyn gave you are perfect if you are allowed to do so.
My current landlord doesn't care what we do to our windows, and in my bedroom I just totally took them down and threw them in the closet. When I move out in a couple weeks, I'll just put it back up.
My next landlord does not allow you to do anything to the blinds (I think she's kind of OCD, but she keeps the place SPARKLING and safe, so I'm willing to deal). You can pull them up a few inches, but any more will bother her. She said "I would like them all to be all the way down and open, but if you have a cat you can pull them up 4 inches". So... I am gonna have to think of something too.
If you put them up that much, then you don't have the problem of climbing through and breaking them, but still the chewing.
Try bitter apple spray on the ends. And make sure the kits have other things that they are allowed to chew on.