ASP.NET MVC checkboxes form GET long query string

I'm using ASP.NET MVC and I have a search form with multiple checkbox controls (about 200) and I send this form using GET request because I need the users to be able to share their search criteria. The problem is that MVC generates the query string parameters for the checkboxes twice (once for true and once for false) and my query string goes very long (about 7000 characters), also IIS blocks my request for having too long query string. I found a way to tell IIS to allow such long query string values using this tutorial: HTTP 400 - Bad Request (Request Header too long). If I upload my app on a shared hosting, I wouldn't have access to machine registry, so this problem is blocking me completely. Have you experienced such a problem and if - how did you solve it? Thanks!