Let's see, time traveling back to prevent the JFK assassination. This is gonna be great. I have total confidence that mature Stephen King will handle this well.
The fact that time travel doesn't actually make sense isn't just something you can sweep under the rug. It really, really doesn't make sense, especially this kind where you can "change" the past. That not making sense isn't just human limitations - it actually doesn't make sense and can't be made to make sense. But luckily we can just ignore that part, by not letting oneself think through the consequences.
The middle is kind of long and nostalgic, the end is ok. The beginning and the setup is the best part, as usual for a King book. It does turn into SF at the end, there, and it's handled pretty well. King is the opposite of authors who drain all mystery out of a story. I was kind of disappointed nobody else was really involved with the assassination.
Why doesn't the hero just write a bunch of letters containing interesting, useful stuff, and send them around?
In general when people time travel, if they know they are going back, they should definitely prepare lots of letters to mail when they get there. Tell people the location of the dead sea scrolls even earlier, and places other lost documents were held or were decaying. There are lots of thousand year old books which managed to survive until 1800, but then decayed just in the last 5 years before being examined.
It'd also be good to tell scientists about the locations of tombs which were raided, so they could get there earlier.