Before revision:  Our first construction is top-down and considers the maximal domain of a worst-case Luxemburg norm. From an applied persepective, this approach can be justified by a uniform-boundedness-type result. In typical situations, the worst-case Orlicz space agrees with the intersection of the corresponding individual Orlicz spaces. Our second construction produces the closure of a space of test random variables with respect to the worst-case Luxemburg norm.
After revision:  Our first construction is top-down and considers the maximal domain of a top-down approach and a bottom-up approach.