"become resident before brexit day, you will be allowed to stay in Spain but not travel elsewhere in the EU" '
l'm not sure that's right - not even in theory - because by that metric a Spanish resident Brit would never be able to drive through France to catch a ferry or even cross the border for a simple weekend break, ultimately who or what will there be to stop them going wherever they want whenever they want anyway?
With no physical borders in the EU for those who aren't flitting back and forth to UK every few weeks it could be a very long time before you got a border check where a passport needed to be produced for scanning or an entry/exit stamp.
I can see driving a UK regged car being a potential problem but if you choose to play that particular game then you have to be prepared for the possible consequences.
It's a point which needs clarifying for sure.