The correct way to do this was to set the parameters one by one.
I created the following method:
public void setSingleValueParameter(String name, String value) {
ParameterValue[] parameter = new ParameterValue[1];
parameter[0] = new ParameterValue();
parameter[0].setName(name);
parameter[0].setValue(value);
service.setExecutionParameters(parameter,"en-us");
}
And then I call the method for each parameter in the order they appear in the SSRS report