I have 2 education names that don't quite fit your criteria. They're not real words, they're brandables, they're misspells that are pronounced the same as a couple of education words that are not a part of your keyword list.
One is a plural, Huge Domains is selling the singular for $18095. The other is 5 letters long. Please PM me if you're interested, I don't want to "spam" you with something that doesn't meet your requirements.
Thanks.