Is there a way to have the floating chat start OPEN?

Yes you can have the floating chat open, you may try this option. Please replace your embedded code.

Please change YOUTHASH (2 places) to your chat hash (8 chars at the end of a chat url when it is opened full screen)

<script>
/* load a floating chat as already opened */
function rt_visibile_chat(hash) {
  setTimeout(
    function () {
      if (RumbleTalkChat && RumbleTalkChat[hash] && RumbleTalkChat[hash].chatDiv) {
        RumbleTalkChat[hash].chatDiv.style.width = RumbleTalkChat[hash].width + 'px';
        RumbleTalkChat[hash].chatDiv.style.height = RumbleTalkChat[hash].height + 'px';
        RumbleTalkChat[hash].chatDiv.style.visibility = 'visible';
        RumbleTalkChat[hash].chatDiv.style.overflow = 'visible';
      }
    },
    100
  );
}
</script>
<div id="rt-387af2133c9f881ba0b77d24032c57e2" data-floating="true" data-side="right" data-width="380" data-height="800" data-image="https://d1pfint8izqszg.cloudfront.net/premium/pricing/chat-icon11.png" data-counter="14:23"></div>
<script src="https://rumbletalk.com/client/?YOURHASH" onload="rt_visibile_chat('YOURHASH')"></script>