Engrossed rhymes with:
grossed, droste, grossed, roast, boast, coast, coste, diagnosed, droste, ghost, grossed, host, ivory-coast, khost, most, ost, post, riposte, roast, toast, toste, voest, woeste, yoast, yost
Engrossed sounds like:
encouraged, encroached, encrust, encrusted