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

Yes you can, you may try this option. Please replace your embeded 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>