I came across the file where I'd isolated and saved Paul F. Thompkins as Alan Thicke and Scott Aukerman singing the theme to "Diff'Rent Strokes on Comedy Bang Bang in 2014.
I contemplated recreating the original opening using footage I could track down of PFT and SA, but instead of wasting my entire day with that, I chose instead to simply lay the audio on top of the video of the original and was pretty impressed at how much it lines up.
Enjoy!
https://www.youtube.com/watch?v=McFgGlFnvhg