[The following is for my own future reference.] I made these in Photoshop using the Timeline and Layers menus. I imported the set of PNG image files via Scripts > Load files as stack. I rearranged my layers and then clicked “Create Frame Animation in the Timeline toolbar > Options ||| > Make frames from layers. I then saved them via Export > Save as Web (Legacy) > GIF.
The following two GIFs were made in Mathematica by defining a Table and Exporting it as a GIF. The animation speeds correspond to the size of the table increments.