Yeah, you can't just move things.... or you'd get strange results for sure.
You'd need a script that would cycle through all the subjects, and when it finds the string you're looking for, move all the threads to the appropriate forum.
Number of threads/posts would need to be adjusted in the w3t_Boards table as well, and as you noticed, there are some other bits (like favorites etc..) that need to be updated.
There is a mass move threads mod here - but you'd have to individually select each thread.
