That is not possible. See also this topic on stackoverflow which gives some explanation: https://stackoverflow.com/questions/1116019/submitting-a-get-form-with-query-string-params-and-hidden-params-disappear
The normal approach would place those fields as hidden input fields. But you say you can't/don't want to do that.
Do you really need to submit your form with the use of 'GET' can't you use 'POST' instead? That could solve your problem also.
There are several other solutions like listening for the submit event of your form and creating the get url yourself (with javascript).