Spoilers
They couldn't use Harry's pillow because:
#1. It'd get noticed pretty easily.
#2. The potion probably took time to make in any case. Polyjuice potion takes a long time to make -- just imagine how much 'bring me back to life' potion takes to make.
#3. Voldemort was planning on returning that night using that very portkey to get into Hogwarts. It makes for a better return to show up at the tri-wizard tournament, rather than show up in the middle of Gryffindor Tower.
#4. Harry Potter and the Pillow of Doom would be a very short book.
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See You In Another Life, Brother.