We show how to evaluate stepwise hedge automata (SHAs) with subtree projection. Since this requires to pass finite state information top-down, we introduce the notion of downward stepwise hedge automata. We then use them in order to define an in-memory and a streaming evaluator with subhedge projection for SHAs. We tune the streaming evaluator so that it can decide membership at the earliest time point. We apply our algorithms to the problem of answering regular XPath queries on XML streams. Our experiments show that subhedge projection can indeed speed up earliest query answering on XML streams.