I finally tried to convert my Cartoon Barry icon into a proper Mac icon.
How did I do it? I followed the instructions on Macapper.com. In short:
(1) Used Photoshop to edit my image into a PNG file with transparency.
(2) Used Icon Composer in Apple Developer tools to create a ICNS file file.
(3) Used Icns2Rsrc to convert that file into a RSRC.
(4) Pressed Apple key plus I and then copied the image to my folder.
Here it is.. You can download it if you like also.
The icon looks like the image in the picture below.