Not missing anything as far as I can see.
OP wants to ED Amherst but it doesn’t mean W&L can’t be ED2 as long as the application is RD/in by Dec1 in time for the Johnson, switched to ED2 (or withdrawn) once the Amherst results are known.
Once the ED Amherst app is done, OP can complete EA at a few private colleges that have it as well as to public universities with merit scholarships.
At this point, universities that want TOEFL/IELTS results should be left to January RD.