With a greedy solver (minimize word pool for the next step), I got ARISE (168) -> BLUDY (13) -> COMET (2) -> NAVAL (1) -> CHUNK.

I think five steps is as good as it gets, as 5*5 is about the size of the alphabet.

Edit: I stand corrected. YEARN (216) -> FLOUT (12) -> CHAMP (1) -> HUMPH.