REMO is the correct route. You need to first get your CMS payment turned into a court order. That court order is then sent to whichever state in the US he resides in and the courts there enforce it.
If he thinks he will escape payment by being in America, he has another think coming. Their enforcement is swifter than in the UK (where the CMS doesn't ever really bite, even though it has the power to). Non payment of maintenance enforced by a US court (which is what REMO does - enforces the order) will be subject to the same penalties as if that court had ordered the payment itself.
E.g. in NY State, they can take his driving licence, take his tax refunds, seize bank accounts/savings, refer to credit agencies (damaging credit), referral to tax office for seizure of assets, denial of business and professional licences (you don't mention his job, but if it needs licences and or relates to finance, these things will be extremely damaging for him); those are just admin enforcements.
When it comes to the enforcement being made by the court, the sanctions are more serious: money judgments, liens, up to three years deposit of maintenance, arrest and prison, because in NY wilful failure to pay child support is a crime.
Different states work differently, so not all will offer the same sanctions - so it will depend on which state he is in. But ultimately, he won't get away with it in the same way as he currently is.