I don't see why you can't use GET, but, serialize/encyrpt the password first. It's easy to do in PHP, but as you have to do it client side, hopefully there is some javascript md5 function.
Another solution would be to send the form data to a hidden iframe which first handles the data. You can then either do what you were intending in the hidden iframe, or you can simply process the URL, use PHP to convert the password to md5 then pass it on to the page you'd originally intended.
The IFrame would redirect to .php?id=&pass=DF098er3DKjD6798daDDF