In my opinion you should look for other solutions, don't just stuck to one solution, there may be other ways.
Reason dropped item changes its position is related to layer change of course.
I have never use drag-drop feature but, did you try something like these;
You can try having a global variable for it, like when mouse over item it changes to 1 or when you drag an item it changes to 1 i don't know. And you can drag items only when that variable is 1.
Just don't change layers it will be a problem, if different layers have different parallax, items will change position whenever they change layer, they even get out of the screen, i suggest you find another solution.
the reason why i am shifting the layer is because if i make it stay at the same layer it stops at its position but as the screen keeps moving, it also moves ahead because its in a parallax layer.
and the variable option you gave, is something like i am using when icon dropped, disable drag and drop for 5 seconds then destroy it and then enable drag and drop again by spawning it at a location at the parallax layer.
but my main problem is still there, i want the icon to stop dead at a place, if anyone has an idea, please help.