Can XMLRPC set show_on_front/page_on_front?

These options are not among the default writable $blog_options.

Here’s one (untested) idea using the xmlrpc_blog_options filter to make the show_on_front option writeable:

/**
 * Add 'show_on_front' to the list of XML-RPC writeable options.
 */

add_filter( 'xmlrpc_blog_options', function( $blog_options ) 
{
    if( is_array( $blog_options ) )
    { 
        $blog_options['show_on_front'] = array(
            'desc'     => __( 'Show on front' ),
            'readonly' => false,
            'option'   => 'show_on_front'
        );
    }
    return $blog_options; 
});

and similar for the page_on_front option.