"Please accept this email as a direct communication from Judge: No change in physical custody. CTM"
First, I disagree that this is not a real ruling. Certainly your attorney can send a full order for the judge to sign, but since this was a "review" hearing then this basically means the judge saw nothing to change their mind about the original ruling. Most order don't have full findings of fact and conclusions of law contained in them. Under Rule 52 of the NC Rules of Civil Procedure findings of fact and conclusions of law are not required unless a party requests them. There are a few types of order where case law has determined they always should be made, but none of those orders are implicated in your facts.
Is there any kind of recourse for me?
You can file for an appeal, although I don't really see what you have to gain by doing so since the judge is still ruling in your favor. You can also file a Motion for Reconsideration but, again, since you won I''m not sure why you would want to do that.
Who can I complain to about this? What will happen if I do?
Can the head family court judge help to compel a decision?
They could, in theory anyway. Most head judges have the power to issue administrative orders to the other judges but whether they can in this case depends on how the head judge was assigned and what was set as their duties. Normally you don't go to a head judge, you go to the court of appeals.
If you want to make any complaints about the judge then your lawyer should draft an order and send it to the judge for signature and, if necessary, set a hearing for entry of the order.
If you want to file a complaint about the judge's ethics you would do so at the NC Judicial Standards Committee at http://www.nccourts.org/Courts/CRS/Councils/JudicialStandards/
However, judges tend to remember these things and it isn't an automatic recusal just because you filed an ethical complaint so the judge could very well be hearing your case again in the future. I don't see an ethical issue here in the facts you've given so my feeling is that the committee wouldn't take any action.
Perhaps you could explain why you believe the judge should have done something else if you were awarded custody and the judge didn't change that?