You should be able to rip using EAC and have MC recognize all the tags, so something is set up wrong. EAC can be challenging and confusing to get set up properly. Unfortunately, I don't really understand what is happening to you, so it is difficult to help. Can you explain in more detail exactly what you are doing and what isn't working correctly? What format are you trying to rip to? What settings are you using? Etc...
On the other hand, Jim does have a very good point. Why not just use MC to rip your discs? It has a secure mode and for just about all purposes is equal in quality and capabilities to EAC, and it is MUCH easier to get set up properly. I generally only pull out EAC if MC can't find the CD data in it's database (which is pretty rare anymore).