No first hand experience, but I doubt travelling on award ticket has any bearing on the compensation amount. Secondly, I doubt that agents have leeway to grant a higher compensation than instructed by LH.
I would be happy to accept a EUR 1,000 comp. for a downgrade from I to PE when on an award ticket and travelling on my own dime; I would also accept the EUR 1,600 comp. for a downgrade to Y. I consider that a fair remuneration for giving up your C seat.