I received an inquiry from a family member today who had been told by the Salt Lake City Cemetery that Archibald is not buried there. I suspect the employee only searched the surname "Gardner." For anyone who would like to know where he is buried, he is listed at the Salt Lake City Cemetery as "Archibald Gardener."
The Utah State Historical Society has a burial database for the state, and you can go to the site to obtain grave numbers for many of the Gardner family members. You will need to try various spellings for the surname to find them all. Archibald is in grave number D 9 6 3 W. The cemetery office has maps and can give you directions to the grave.
Below are pictures of several of the original grave markers in the Gardner family plot in Salt Lake. Many of the markers had been lost over time, so a project was done in the 1990s to place a new marker and identify all family members who are buried there. Archibald's original marker is being preserved at the museum at Gardner Village in West Jordan, Utah.