As stated in http://www.boutell.com/newfaq/misc/urllength.html, HTTP query string have limited length. It can be limited by the client (Firefox, IE, ...), the server (Apache
REST is a manner to do things, not a protocol. Even if you dislike to POST when it is really a GET, it will work.
If you will/must stay with the "standard" definition of GET, POST, etc. than maybe consider to POST a query, that query will be stored on the server with a query id and request the query later with GET by id.