There are not only directly EASA approved ATOs in the US. Several operate as satellites of UK ATOs, CTC and others in Phoenix, for instance, and Naples Air Center in Florida, quite possibly others. You really need past student recommendations for US schools as the quality can be highly variable, and even the designated examiners the ATO uses can make a difference. You would have to talk to your chosen ATO about using the family C172, some might say yes, others no. One objection might be if the test is to be taken in an Arrow a then Warrior is a better lead in aircraft than a C172.