It would never be a bad idea to pull all the engine related relays apart (and their wires) for inspection.
I’m interested to know why the fuel pressure is dropping. It should be a constant 3 bar full time (under load or not) what happens when you remove the vacuum to the fuel pressure regulator and then go for a drive? Do you have the luxury of watching the gauge whilst driving?
The fact that it goes down to 2 bar is concerning but, doesn’t seem to account for the rough running
Further diagnosing is necessary.