Ken Mcdonald over on the JoomlaCode forums was kind enough to help me out:
In AVR Manage Players edit the Vimeo player and add the code in bold below:
<script type="text/javascript">
swfobject.embedSWF('
www.vimeo.com/moogaloop.swf?clip_id=@COD...;autoplay=@AUTOSTART!d@&fullscreen=@USEFULLSCREEN!d@
&hd_off=1','@DIVID@','@WIDTH@','@HEIGHT@','9.0.28',@XPINST@,
false,{wmode:'@WMODE@',allowfullscreen:'true',scale:'showall',bgcolor:'@BGCOLOR@',menu:'@MENU@'},{id:'p_@DIVID@',styleclass:'@AVCSS@'});
</script>