The solution turns out to be so simple that it ill make people laugh at me.
Scrap all of the javascript and operate solely with the template. Recall that the code line, <img src = "../../images/RCG15_edited.png" , &c., installs Jesse Black (or whoever you have for RCG15) above each and every round.
Now, the strange Double-dollar function SOMETIMES works by incrementing itself, round by round, but sometimes does not. The good news is that here, for me at least, it does.
So, rather than try functions in the form, <img id = (some value)..., we simply can set the <td id and the img src to the double-dollar function.
Here is the whole code (which installs at the beginning of the 6th template, BoutLogRoundStart.tpl ):
<table border="0" width="100%" height="440" align="center" bgcolor="000000" cellspacing="0" cellpadding="0";>
<tbody>
<tr>
<td id = "RCG$$No$$">
<img src="http://www.ootpdevelopments.com/images/RCG$$No$$_edited.png" height="440"; style="vertical-align:bottom; padding-left:5px;"/></td>
<td width="100%"; class="rest"; style="padding-left:0px;" align="left"></td>
</tr>
</tbody>
</table>
N.B.: The subelement, "class='rest';" installs the background image, which for the WTBA is the two topless girlfighters in black and white. I will assume that most people here want something else (or nothing at all). You can remove this snippet (but keep one of the semi-colons!) to get nothing (you may get nothing anyway), or you can install your own substitute in the documents folder, ../../Saved Games/[universe name]/images , or (for some) ../../Saved Games/[universe name]/Bouts/images .