I only needed to be more persistent in my Googling... Found out how to launch a script immediately upon a screen starting. To do this:
1) Create a script button, as described above to perform the actions you wish.
2) Click on the new button to get the ID from the "Properties" section of the screen
3) Copy the ID
4) Click on the background (or "UserArea")
5) In the properties section, paste the script button ID into the "OnCreateHandler" variable.
Done! Now when the t-code is called, the script button is automatically pressed! Now to hide the button so make the screen look pretty!
Thanks Chris for kick-starting my journey!