Generate different code in wp_footer for each shortcode instance

I created a WordPress plug which provides a custom post type (Slides) and these can be grouped by a taxonomy (Slideshows). Using a shortcode [slides], you can display these Slides and filter them by Slideshow. Here’s how I coded the shortcode:

function slds_shortcode( $atts ) {
  extract( shortcode_atts( array(
    'slideshow' =>   'all',
    'timeout'   =>  '5000',
  ), $atts ) );
  $slideshow = $atts[slideshow];
  global $post;
  $tmp_post = $post;
  $args = array( 'slideshows' => $slideshow, 'timeout' => $timeout, );
  $myposts = get_posts( $args );
  ob_start(); // Helps output the HTML where the shortcode is (otherwise it outputs before the content).
      ?>
  <div id="<?php echo $slideshow; ?>" class="slds-slideshow">
    <div class="timeout-<?php echo $timeout; ?>">
    <?php foreach( $myposts as $post ) : setup_postdata($post); ?>
      <div class="slide"> 
      <?php the_content(); ?>
      </div>
    <?php endforeach; ?>
    </div>
  </div>
  <?php
  $post = $tmp_post;
    return ob_get_clean();
}    
add_shortcode('slides', 'slds_shortcode');

The scripts and stylesheet are included in the footer, only if a shortcode is found in the post. The script (responsiveslides.js) requires an init, which currently outputs in the footer whether a shortcode is found in the post or not. Here’s how I generate that:

function slds_init() {
  echo '
  <script>
    jQuery(function($) {
      $(document).ready(function() {
        $(".slds-slideshow .timeout-5000").responsiveSlides({
          pause: true,
          nav: true,
          pager: true,
          timeout: 5000,
          speed: 1800
        });
        $(".slds-slideshow .timeout-10000").responsiveSlides({
          pause: true,
          nav: true,
          pager: true,
          timeout: 10000,
          speed: 1800
        });
      });
    });
  </script>';
  }
add_action('wp_footer', 'slds_init');

This works great, so long as the defaults I coded in there are suitable for the project. Instead, I’d like to be able to set these parameters in the shortcode like: [slides slideshow=tour timeout=10000 speed=1200]. As you can see above, the init has a few major limitations. It selects ALL instances of .slds-slideshow instead of selecting each shortcode output individually by a unique id or class, meaning these default parameters have to be used for all shortcode outputs. In fact, the reason I have two jQuery selectors is so I can add an alternate .timeout class to the output, which just changes which jQuery selector is affecting the shortcode output (or slideshow HTML if you will). This is a shoddy solution. Obviously if I relied on classes for all the parameters this way, with the virtually infinite number of parameter combinations, the init would become extremely heavy and clunky.

How can I generate that middle section of the init (the jQuery selectors and their parameters) based on the shortcode attributes in such a way that they still correlate to the HTML output of the shortcodes in the post?

Edit

Thanks again @birgire for your ideas! I think they got me much closer to where I need to be.

I tried out a lot of options. I think the main thing I’m still running into is getting shortcode instances to generate anything in my javascript initialization. I put wp_localize_script() in my shortcode function as @birgire suggested:

wp_localize_script('slds_script', 'slds_vars', array(
  'instance' => $instance,
  'timeout'  => $timeout,
  'speed'    => $speed
));

So with two shortcodes on the page with timeout and speed set differently, I now get:

/* <![CDATA[ */
var avrgslds_vars = {"instance":"53442837d55c2","timeout":"10000","speed":"500"};
var avrgslds_vars = {"instance":"5344283814479","timeout":"5000","speed":"200"};
/* ]]> */

(I set a new variable for the instance: $instance = uniqid();)

That seems like a significant improvement! So in my javascript initialization, I tried echoing a variable set in my shortcode, which would have all the shortcode “atts” (parameters):

$jQselectors = "";
$jQselectors .= " // Hoping this will keep the array keys from overwriting eachother.
  $(slds_vars.instance).responsiveSlides({
    pause: true,
    nav: true,
    pager: true,
    timeout: $timeout,
    speed: $speed
  });
";

Of course, I realized after I saw this result…

<script>
  jQuery(function($) {
    $(document).ready(function() {
    });
  });
</script>

I can’t select the variable from outside my shortcode function like I was attempt to do:

function slds_init() { ?>
  <script>
    jQuery(function($) {
      $(document).ready(function() {
<?php echo $jQselectors; ?>
      });
    });
  </script>
<?php 
}    
add_action('wp_footer', 'slds_init');  }

I’m having trouble wrapping my head around how to do this. I may just have a misunderstanding on how arrays work. Any ideas? Any/all help is greatly appreciated.