I don't think you'll be able to use the scripts verbatim, so you'll have to dig enough to be able to grasp what they are doing (not the same at all as being able to generate it). I hope the following is at the right level for you. I'm working off your phrase, "if any modifications are recommended" and I know that nothing above will work for you without modifications.
I would start by working on creating a script that will report to you what the position value is (combined x and y) for some specific icon on your desktop. In your case, it's the same situation all the time, so you could hard-code the name, rather than worrying about how to find or query for the name. At the very beginning of this thread, there is an example of AppleScript syntax for specifying desktop icons instead of Finder icons so that's part of your starting point.
When you are able get and display the position of the icon you want to move, make a note of the position value (x and y) for both of your target positions, where you want the icons placed. Then try modifying the AppleScript to set the value rather than geting it, to see if you can move it with your script. When you can do that, you're more than halfway home.
UPDATE: I was totally focussed on "the scripts above" and overlooked the reference to another thread:
That thread has two answers, one from @peternlewis about doing it entirely with KBM, in which he notes:
Then second answer from @ccstone uses AppleScript and does what I described above. It looks like it's exactly what you need.