Actually, I just figured out a way to do it with a bit of manual code and then getResources... here's what I did.
In the Sponsors page, I added the following code:
<table width="680px">
<tr>
[[getResources? &parents=`13` &tpl=`getResourceLinkWithImageTblTpl` &tpl_n3=`getResourceLinkWithImageTbl3Tpl` &limit=`0` &sortby=`-menuindex` &showHidden=`1`]]
</tr>
</table>
I've manually defined that I will be using a table and set a fixed width. I then call out the definition for the first row and had the processing over to getResources. The primary TPL will be called with the secondary TPL being called for every third record that it finds. The TPLs look like this:
Primary
<td width="225" align="center">
<a href=[[~[[+id]]]] [[+link_attributes]]><img src="[[+description]]"></a><br>
</td>
Secondary
<td width="225" align="center">
<a href=[[~[[+id]]]] [[+link_attributes]]><img src="[[+description]]"></a><br>
</td>
</tr>
<tr>
Once the getResources processing is done, the Sponsors page inserts a row close and a table close. For me, I end up with an extra row at the bottom, but this isn't an issue for me as my table is at the end of my page and I do not use borders. I could have gone a step further to add the &tplLast and use THAT to close the row AND the table, and likely will, but this hits what I was searching for pretty easily.