The best I could do with today's word, and the wordlist, but no scoring function to minmax the rules:

- FUFFY (8159) (shipping of Faith and Buffy from Buffy the Vampire Slayer)

- IMMIX (4544) (to mix or blend)

- ZOCCO (2142) (low plinth, from the Italian word for sock)

- QAJAQ (530) (alternative form of kayak)

- TRATT (155) (clipping of trattoria)

- KHAPH (7) (alternative form of khaf, the 11th letter of the Hebrew alphabet)

I get the feeling that if this game had 7 steps instead of 6, it would almost always be impossible.

I had two word possibilities left at the end, so it's possible.