How can I set up Eclipse/eGit/GitHub in a way that is easy for students?
To me it sounds like your students lack an understanding of the fundamentals of IDEs and Git.


  if I ask them to use the command line, they will never do it.


If they don't know git init and git clone (origin) then I'm sorry, they do not know Git, they should learn this first (along with push, pull, commit, status, fetch).


  Researching this, the stock advice seems to be to set up the repository outside of the Eclipse project. That, however, has the effect of putting all the source code outside of the Eclipse workspace, which is confusing. Worse yet, I can't then import the project correctly into another Eclipse environment.


This is another problem in itself. The high level explanation is you only need package level codebase with only the src, the bin is generated by Eclipse. You still need to create a project in Eclipse and then import the package. Any further problems should be asked on StackOverflow.


  The other method would be to put the repository (and .git) under the Eclipse project.


NO! The .git is generated by git init. Do not copy any configuration, especially hidden files from project to project.

I think you are jumping the gun here. Eclipse and Git should be separate lessons. If they are confused by both then that just means they need to learn what each of them are, before combining them.

I suggest:
Teach Eclipse, how to create projects, what packages mean, how to import, etc.
Teach Git, init, clone, pull, commit, push, status, fetch using Terminal or CommandLine for Git. Depending on the age group you might want to teach them how to resolve conflicts, what decentralized means, branching, pull requests, etc.
Now teach them Eclipse Marketplace, download plugin and integrate Git with Eclipse.


  So does anyone have a setup for Eclipse and eGit that successfully puts the entire project into version control, and is not confusing for students? And that allows the project to correctly import into Eclipse?


As all my professors do it, you need to create the repository with the project for each student and have each student clone and import into Eclipse. I'm not an educator so I don't know if there is an existing setup available online. However, I do think this is actually a very trivial task if they understand Eclipse and Git.