HTML FORMs are limited to www-form-encoded or multipart. The length or the queries on a GET with a FORM is limited by intermediaries that shouldn't be limiting it. But that's reality.

Do a POST of a query document/media type that returns a "Location" that contains the query resource that the server created as well as the data (or some of it) with appropriate link elements to drive the client to receive the remainder of the query.

In this case, the POST is "writing" a query resource to the server and the server is dealing with that query resource and returning the resulting information.