In fact, it's the other way around.
Burntrap is actually The Mimic, or one of the Glamrock Endo's infected with the Mimic1 program, that infused itself with Aftons corpse. William is long dead, burning in Ultimate Custom Night for his deeds.
In the Tales From The Pizzaplex books, we see how the Mimic was created ("The Mimic") and how it affected the pizzaplex ("Tiger Rock". "The Storyteller").
We see in the very first epilogue that the Mimic was locked in an underground section of the Pizzaplex when it misunderstood its programming and started killing people. This is why The Mimic runs after Cassie: it thinks she's an endoskeleton and must be destroyed, just like its programming says.
Hope this helps!