This works:

DesktopOK 5.18 . . . Save and restore the desktop icon positions . . . https://www.softwareok.com/?seite=Freeware/DesktopOK

Which program do you use or recommend to backup icon layout?

EDIT: I seem to have found a solution to this problem. When on the desktop, right click and hover over "View" and make sure "Align to Grid" is UNCHECKED and off. No more random icon rendering every time you switch screens. I do however recommend a program to backup your icon layout just in case something happens so you can just restore them to their previous settings.

Today I came across Dexpot, and decided to try it out. After hours of organizing my icons between my "new 3 desktops", I've come across a major bug with the program that seems to be a make or break for me to use it... I have "Customizable desktops" turned on, and my default desktop is set as the "Desktop 1", however whenever I switch desktops then go back to desktop #1, my icons spazz out for a second before returning back in place, however somewhere in the middle of the group, one of the icons will pushed down a "column", pushing everything else after it downwards with it. Basically, my icons on Desktop #1 keep rearranging themselves and I have no idea how to fix it... I've tried restarting the program & computer, running it as administrator, and rearranging the icons. This problem is ONLY occurring on Desktop 1, and when I close out of Dexpot the icons remain in place where they should... Running the latest version of Dexpot & Windows 8.1 on a 64x system. Any ideas?