I knew about the subtract/weld feature in the Pazzles software, but I never really used it except for when I was learning how to use the features back in 2011. After watching Youtube videos of people doing what I wanted to do in other software, the light bulb in my head went on!
Below are instructions for Pazzles, SCAL 3, and MTC.
Note the different names on the videos: Subtract/Weld in Pazzles, Path>Union in SCAL 3, and Boolean Join in Make-The-Cut. They serve the same purpose.
Pazzles Inspiration Studio Pro 2010 (with updates)
Make-The-Cut Version 4.6.1
Make your own silhouettes - Video Instructions