I don't think TJ attacking Carl contradicts anything, it's clear he's heavily repressing the memories of Sydney's death so even if he was the one behind the treasure hunt he probably wouldn't have been all there mentally while setting it up, he might have even been influenced by the town.
It's true he was often with Chase during the day but he still had plenty of opportunities to do it, especially at night. It's also possible he might not even have set it up during their trip to Echo but instead while he was still a kid, which would explain why the letters look old if it's not done purposefully. Another thing that points toward TJ is that he had a pretty clear chance to put the letter that begins the treasure hunt in Carl's crawlspace during the birthday party since he went searching downstairs.
Concerning the hysteria and the entity I don't think we have enough information about them to make an accurate guess on how they operate, if anything the entity controlling Chase was pushing him towards concealing the truth not revealing it.