lhungil:
As your "theme" (template files, overrides, and other bundled changes) is a commercial product, you may wish to contact the vendor for further support if fixes / changes to the "theme" are needed.
Updating the "theme" / template files to use "HTTP_SERVER . DIR_WS_CATALOG" instead of "zen_href_link(FILENAME_DEFAULT)" would work.¹ This is what most templates (and Zen Cart's stock template) use when creating the home link. I would suggest altering the theme you purchased to use this instead of going down the "alternative" URLs rabbit hole (unless you have other business reasons to desire alternative URLs).²
In the future Zen Cart may natively support "zen_href_link(FILENAME_DEFAULT)" outputting "/" instead of "/index.php?main_page=index".³
Aye, the code from Ultimate URLs and CEON URI take a look at the URL and will typically handle "zen_href_link(FILENAME_DEFAULT)" by outputting either "HTTP_SERVER . DIR_WS_CATALOG" or "HTTPS_SERVER . DIR_WS_HTTPS_CATALOG" followed by the zenid parameter if needed.
Just a heads up, once you go down the "alternative" URLs rabbit hole... Make sure your theme includes canonical link support. The DEMO for the theme you mentioned appears to support. No way to know for sure if the one on your site does without a link to your site.
NOTE 1: There are some other places internally where Zen Cart does actually use "zen_href_link(FILENAME_DEFAULT)", which does handle certain scenarios with sessions better than "HTTP_SERVER . DIR_WS_CATALOG"... However the affected scenarios are rare.
NOTE 2: I do use alternative URLs on a number of Zen Cart websites, so not saying there are not good business reasons to install and use a tool such as "Ultimate URLs". I am just saying it is overkill if all you wanted to do was have the home link in the header / footer navigation omit "index.php?main_page=index" from the URL.
NOTE 3: Some initial changes have been committed to the Zen Cart 1.6.x development branch to accommodate "zen_href_link(FILENAME_DEFAULT)" outputting the site URL without the "index.php?main_page=index". But keep in mind those changes are not final at this time (and I would not recommend applying them to a production store unless one understands all the potential implications).
I uninstalled the Ultimate URL's since it sounds like it isn't such a good idea. I then replaced "zen_href_link(FILENAME_DEFAULT)" to "HTTP_SERVER . DIR_WS_CATALOG" and that fixed my problem. Thank you so much!