This is not expert advice, but I think you can co a few things:
Apply for a passport for your son when you naturalize and see what Department of State does.
Apply for N-600 to get a certificate of citizenship for him and see what USCIS does about it.
Try to get legal custody of your son.
I think overall you have a good case as your son has been living with you all the time. I am not sure how picky USCIS or Department of State are about the legal custody part, but assume that they might be serious.
Here is an excerpt from a page I found:
Both section 320 (automatic derivation of citizenship) and 322 (citizenship on application) require that the child be in the "legal custody" of a U.S. citizen parent. Under the regulations, the INS will presume that a U.S. citizen parent has legal custody in the following situations: (1) where "a biological child . . . currently resides with both natural parents (who are married to each other, living in marital union, and not separated)"; (2) where "a biological child . . . currently resides with a surviving natural parent (if the other parent is deceased)"; or (3) where "a biological child born out of wedlock . . . has been legitimated and currently resides with the natural parent."
In cases of adopted children, the INS will find that a citizen parent has legal custody "based on the existence of a final adoption decree." In cases of a child of divorced or legally separated parents, the INS will consider a citizen parent to have legal custody where the parent has been granted "an award of primary care, control, and maintenance" of the child by a court of law or other appropriate government entity. Where there is an award of "joint custody," the INS will consider both parents to have legal custody. In cases where the issue of custody is not explicitly addressed in a divorce decree or a separation agreement, the determination of legal or joint custody will be based on the laws of the state or country of residence. The regulations state that "[t]here may be other circumstances under which the Service will find the U.S. citizen parent to have legal custody for purposes of the CCA."
http://www.nilc.org/immlawpolicy/natzcitzshp/nc035.htm