Yeah that was my theory too, and the way the drawing in the final letter seems to have been drawn in TJ's style (like the one he drew at the diner). However one major problem with the theory is that if it was TJ who drew it, it wouldn't have made sense for him to go berserk on Carl at the end. Also it wouldn't have made sense that TJ did it in terms of the timeline. Chase was pretty much always with TJ all throughout the route so he wouldn't have had the time to sneak away and set it all up.
At most, TJ could have drawn the final drawing, and then one of the entities took it and put it in the last area as a way to trigger the hysteria. The evidence for this comes from Flynn's route, when the gang found out that Chase was the killer and the hysteria began immediately (which we're assuming is what the entity wants). So when Chase swapped out the drawings, the hysteria was narrowly avoided and the entity was forced to directly manipulate Chase (through the mirror). As a result the hysteria was delayed to 2017 based on the epilogue.