This is becoming very confusing, because the procedure under CCP sect 2029.010 is essentially the same as if you were getting documents pursuant to subpoena within California (start reading at CCP sect. 2020.210).
Was the notice of deposition issued by the out-of-state court? And is the "defendant" on whom it was served the company in Marina Del Rey? And if it was served, what did it command? And if it was served on the Marina Del Rey company, what was the response.
Was the subpoena issued by the out-of-state court? Was it a production subpoena?
By "buy the supoena", I am guessing that they are telling you that you can purchase the form for a Supoena for the Production of Documents from them. That's only a few cents and you can also download it from the California Judicial Council web site for free.
Did you file a Civil Cover Sheet to "register the out-of-state subpoena"? (Can't think of any other way to ask the reason for the Cover Sheet.)
Without your answers, this is where I THINK this is going:
You should be able to serve a California Supoena for Production of Documents on the company. Direct production to a "deposition officer", such as a local court reporting firm, for copying. Note that if the Marina Del Rey company is not a party to the action, you'll have to also tender an offer to pay production costs to bind them to comply (read the statutes).
I could imagine registering the sister-state order with the California court so that, if there is non-compliance, there is a basis for citing the company into court for contempt. It's possible that the Court also feels that a hearing is required to register the order. If that's the case, ask for an ex parte (expedited) hearing
I can't imagine the reason for the Cover Sheet but it appears that, in some way the Court is trying to gain authority to enforce it's own orders.
This is a lot of guessing, because I'm trying to make sense out of what you've described.
Are you acting as your own attorneys? (With due respect, that might account for some of the confusion.)
Have you talked to the Civil Supervisor or just any clerk who will talk to you? If you haven't done so, ask to talk to the Supervisor or the Civil Law Clerk. Court employees are not permitted to give you advice but, if the Court itself is saying that it doesn't know how to deal with this, go to one of the two people who have the final word on what needs to be done. As a matter of fact, if you haven't talked to one of these two, do it before trying to answer my questions. And go to Court and do it directly rather than by phone.