You can boost your EMS by using the Mini game at N7 HQ. Login with the same credentials you use for Origin and then choose "Galaxy at War"
Here you can play the Mini Game that pushes the "Readiness Rating" up, exactly like playing MP would do.
For the EMS, you can obtain max 3750 EMS in a game without any DLC's, so reaching the 3100 EMS needed if you have the "Extended Cut" installed is possible.
To be honest I always found it to easy to get the EMS score you need after the EC was released, but I also never lost someone (exept Wrex) in the first and second game.
Also important to note you have to achieve the required EMS before going to Cronos Station. That's when you're locked in.
