Maybe you should try changing the name on the buttons to be more clear. 'New Post' does not necessarily tell me if I'm making a new post on the current thread or creating a new thread. Try something like 'Post new topic' and 'Post reply'.
> I am thinking about taking the 'New post' button off the thread page entirely and only leaving the option to Reply.
Sure why not. We have it that way for years now, never had any complaints. It's the inconvenience of threads in the wrong forum against the inconvenience of needing to click once more to make a new thread. I choose the latter.