Well, I never figured out how to get the rss version of the feed to work properly, but I did indeed get the atom feed to work. That, I guess, is enough for me.
The good news is, I figured out how to stop the rss feed option from showing in the browser. The file to edit is in this path:
/(your site)/components/com_content/views/category/view.html.php
and
/(your site)/components/com_content/views/section/view.html.php
To stop the rss option, you want to remove:
$attribs = array('type' => 'application/rss+xml', 'title' => 'RSS 2.0');
$document->addHeadLink(JRoute::_($link.'&type=rss'), 'alternate', 'rel', $attribs);
To stop the atom option, you want to remove:
$attribs = array('type' => 'application/atom+xml', 'title' => 'Atom 1.0');
$document->addHeadLink(JRoute::_($link.'&type=atom'), 'alternate', 'rel', $attribs);
This will allow you to select the show feed option, without using the syndicate model, to have the feed icon show in the browser for the page you have set a feed for. It allows you to select either the rss, or, the atom feed option (in my case the atom because it was the only one that worked correctly) but not both as it is set to do as default.
I hope this helps anyone who may have this same issue.