Change Content for Specific Page

Your function is signup but you’re hooking check_for_signup. You’re also trying to apply the_content filters from within a function that’s hooked to the_content:

function wpse_225562_replace_for_signup( $content ) {
    if ( strcmp( 'signup_slug', get_post_field( 'post_name' ) ) === 0 ) {
        $content="Sign up, bitch.";
    }

    return $content;
}

add_filter( 'the_content', 'wpse_225562_replace_for_signup' );

Here we are simply hooking to the_content and replacing the passed-through $content with something else if the current page is signup_slug – hope that makes sense?