How about: All pieces decrease in value each time a player is eliminated. Q: 9->5->1, R/B: 5->3->1, N: 3->2->1 p: 1->1->1.
I'd imagine this will encourage early trades! With two players left, each piece will only be worth 1 point. Additionally, with all 4 players alive, opposite's material/mating him is worth double, or ~1.5x with 3).
Another idea: somehow compensate for being in the middle during the 3player phase.
But why not " the winner takes it all"?