I am not a lawyer, but I would recommend against having the full text of the MIT License in both the README and LICENSE files. Just like with real code, duplication can be a maintenance hazard. If you feel that you must talk about the license in the README, I would just state the copyright and that the project is licensed under the MIT License and leave it at that.
does this mean people who create derivative works cannot change the license text in the README? Or does this only apply to the LICENSE file?
The MIT/X11 License makes no restrictions on where the license text must appear for a given project. I think one would be free to change the text of the license within the README as long as an unmodified version of the text is intact somewhere within the project (e.g. the LICENSE file). Would this be confusing to have two different wordings of the license? Absolutely! However, I don't think you are prevented from doing so.
Is MIT even appropriate for projects of this type?
Sure, it's appropriate, but what are you trying to accomplish with your license? If your goal is to protect your copyright on README, then it seems like a reasonable choice. However, others may add their copyright to the README if they make modifications/additions.