Here's my workaround, this is a solution to these issues:
You can't install m2e-egit (I get an error in Juno)
Converting a general project (connected to your Git repository) to a Maven project isn't working for you (The Import Maven Projects step seems essential)
Importing Maven Projects from your repository on the filesystem isn't showing the project connected to Git.
Setup your Git repository in the Git Repository Exploring perspective.
Switch to the Java perspective, Import > Existing Maven Projects
Browse to your Git checkout in the filesystem, select the directory containing the pom.xml file. Finish the import;
you'll notice these projects aren't connected to Git. :-(
Delete these projects, but DO NOT DELETE FROM FILESYSTEM.
We don't want our clone deleted; this task also leaves the .project file behind so that we can import in the next step.
Go back to the Git Repository Exploring perspective.
Right-click your repository, Import Projects...
Select Import existing projects
In the explorer below, browse to and select the directory containing the pom.xml (and .project file) , then click next.