Three.JS rotate projection so that the y axis becomes the z-axis

You could just change the camera rather than the entire coordinate system. For example:

var WIDTH = 1024;
var HEIGHT = 768;
var VIEW_ANGLE = 45;
var ASPECT = WIDTH / HEIGHT;
var NEAR = 0.1;
var FAR = 10000;
camera = new THREE.PerspectiveCamera(VIEW_ANGLE, ASPECT, NEAR, FAR);
camera.position.z = 300;
camera.up = new THREE.Vector3( 0, 0, 1 );
scene.add(camera);

This changes the up vector for the camera to use Z-UP.

EDIT:

To illustrate an example, here’s the jsfiddle you created slightly modified to call lookAt after setting the up vector: http://jsfiddle.net/NycWc/1/