One thing before i answer your question: Did you apply for H4 COS too? or got your H4 stamped by going outside USA before applying for H4-EAD?
If you did apply for H4 COS, then your H4EAD is waiting for H4 COS first and it is taking a hell lot of time. You probably are better off going out of USA to get H4 at this time.
If you already had H4, then there is no specific reason except that the USCIS officer working on your case is busy with other cases in his queue. Your turn will come sooner or later.
So, your better option is to go out of USA and get H4 stamped. Once you go out, your H4 COS will be automatically abandoned by USCIS.
Re-enter USA on H4 - Wait for H4 EAD result
Then, you will have to re-enter USA with H4 visa. After this, your existing H4 EAD application might receive RFE to prove H4 status.
At that time, you can submit your H4 status proof.
Submit another H4 EAD application - fast track with H4 status
Or, if you do not want to wait for RFE, you can file another H4 EAD application with H4 status.