I was able to ‘fix’ this problem by removing the query string from the script include in wp-admin/admin-header.php
that is, I changed:
<script type="text/javascript" src="../wp-includes/js/tinymce/tiny_mce_gzip.php?ver=20051211"></script>
to
<script type="text/javascript" src="../wp-includes/js/tinymce/tiny_mce_gzip.php"></script>
(around line 50)
I don’t know if there are any detrimental effects from this, but it does appear to have worked….