Changes in Perch layout (template) content not refreshing

I have Perch 2 up and running on a client site that is getting pretty close to going live, and I am having a problem making edits to content templates.

I have edited two different custom content templates [ eg: /perch --> /templates --> /template_name.html ] and when I go to make html edits to the templates nothing happens on the site. I have tested to make sure the changes in the code are 'taking' by logging in to my host and accessing the files that way (rather than via ftp) to ensure my host is serving them correctly, and they are. But when I use developer tools I can see that Perch is inserting the old/wrong code into the pages.

What do I need to do to make Perch serve the updated html to the pages where the content templates are inserted?

Here's an example of one of my templates that won't update — previously it included a link to Pinterest, then I removed that link, but it still shows up on the site despite not being in the template when I access the file:

<ul class="social-share">
    <li><a href="<perch:content id="facebook" type="text" label="Facebook Link" />"><i class="fa fa-facebook"></i></a></li>
    <li><a href="<perch:content id="twitter" type="text" label="Twitter Link" />"><i class="fa fa-twitter"></i></a></li>
    <li><a href="<perch:content id="instagram" type="text" label="Instagram Link" />"><i class="fa fa-instagram"></i></a></li>
    <li><a href="<perch:content id="googleplus" type="text" label="Google Plus Link" />"><i class="fa fa-google-plus"></i></a></li>
</ul>

It doesn't get much simpler than that, so I'm really at a loss. Here's the code (that I'm pulling from Chrome developer tools) that's showing up in the live site, regardless of how many times I clear my cache:

<ul class="social-share">
    <li><a href="https://www.facebook.com/terryhoagevineyards"><i class="fa fa-facebook"></i></a></li>
    <li><a href="https://twitter.com/TH__EstateWines"><i class="fa fa-twitter"></i></a></li>
    <li><a href="https://www.pinterest.com/THVineyards/"><i class="fa fa-pinterest"></i></a></li> 
    <li><a href="https://instagram.com/th_estatewines"><i class="fa fa-instagram"></i></a></li>
    <li><a href="https://plus.google.com/u/0/+THVineyards"><i class="fa fa-google-plus"></i></a></li>
</ul>

???

Here's my diagnostic report:

Perch: 2.8.6, PHP: 5.5.21, MySQL: 5.1.73, with PDO
Server OS: Linux, cgi-fcgi
Installed apps: content (2.8.6), assets (2.8.6), categories (2.8.6), perch_events (1.9.2)
App runtimes: <?php $apps_list = array( 'content', 'categories', 'perch_events', );
PERCH_LOGINPATH: /perch
PERCH_PATH: /nfs/c11/h05/mnt/205986/domains/thestatewines.com/html/perch
PERCH_CORE: /nfs/c11/h05/mnt/205986/domains/thestatewines.com/html/perch/core
PERCH_RESFILEPATH: /nfs/c11/h05/mnt/205986/domains/thestatewines.com/html/perch/resources
Image manipulation: GD
PHP limits: Max upload 2M, Max POST 8M, Memory: 99M, Total max file upload: 2M
Resource folder writeable: Yes
HTTP_HOST: thestatewines.com
DOCUMENT_ROOT: /home/205986/domains/thestatewines.com/html
REQUEST_URI: /perch/core/settings/diagnostics/
SCRIPT_NAME: /perch/core/settings/diagnostics/index.php