You already answered yourself: Union Libre or Concubinage.
By DR Law, you and your partner "are married" or "living formally together"
You guys can formalize your relationship by an "Acto de Union Libre" certified with a lawyer and a notary.
But before that, ask to a lawyer if this affect your legal status in the US.
By DR law Union Libre/Concubinage is NOT marriage. There is NO common law marriage in the DR. It simply does not exist.
I have a sister in law that lived in concubinage for decades. When the man died , the woman got NOTHING despite going to court.
His children got EVERYTHING. No piece of paper from a lawyer would have changed that.
Will a lawyer take your money to come up with a meaningless paper for your Union Libre? I bet they would.
For the OP to get what he wants, he has to create a will since he does not want to get legally married because he would lost US benefits.
The only way he would lose US benefits is if he got married.