Update!
Bought myself a clay bar today, and after washing the car I went to work on the paint drops..
It works, well, kinda. To remove a small paint drop, it takes between 4 and 7 minutes
per spot, and I have literally thousands of them.
I can see the red paint getting into the clay, but the larger paint drops are taking a couple of eternities to remove.
I'm out of ideas, I really thought the clay would work, but not that slow... Leaves the aint shiny though!