Moving particles from one object to another... in order...

[Gregory]

Hey, lovely coins and render!

Thanks. 
Though, I like Drawer14 solution better, and I wish I had know it before I created coins. 

Not sure what you want exactly, and what you mean by elegant. If you don't want a PhysX collision, then just move them (gently) where you want them without PhysX. 
Operators like custom properties, find target, particles properties, surface test, etc are your friends. 
You can try using neighbors in particle properties operator, to test particles distance, and move them. 

Again, not really sure what exact motion you want there, but should be doable without problem.

Thanks for the suggestions.
I'll give it a try, but tbh any kind of solution (clean or not) that can get me the result in that posted video, would make me very happy.
That particular setup troubles me for quite some time now.