Move jQuery to the bottom of the page whilst keeping the WordPress jQuery

You can change it by calling add_data method of $wp_scripts object. This object holds all scripts and information how to render it. To force rendering script in the footer you can do it like this:

add_action( 'wp_enqueue_scripts', 'wpse8170_enqueue_scripts' );
function wpse8170_enqueue_scripts() {
    $GLOBALS["wp_scripts"]->add_data( 'jquery', 'group', 1 );
}

P.S.: I haven’t tested it, but suppose it has to work.