Hey James,
I appreciate all of your help with this. I don't want to waste your time anymore on this topic. In the flypage.tpl, the call for the add to cart looks like this:
<td colspan="2"><br /><?php echo $addtocart ?>
I changed it to:
<td><br /><?php echo $addtocart ?>
...and it seems to be fine now. By the way, I haven't changed it on the site in question, but on another that was just launched. I'm just assuming that it will work for the other site to because it's using the same flypage.
Once again, thanks for all of your help on this.