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Intelligent voice assistants, such as Apple Siri and Amazon Alexa, are widely used nowadays. These task-oriented dialogue systems require a semantic parsing module in order to process user utterances and understand the action to be performed. This semantic parsing component was initially implemented by rule-based or statistical slot-filling approaches for processing simple queries; however, the appearance of more complex utterances demanded the application of shift-reduce parsers or sequence-to-sequence models. Although shift-reduce approaches were initially considered the most promising option, the emergence of sequence-to-sequence neural systems has propelled them to the forefront as the highest-performing method for this particular task. In this article, we advance the research on shift-reduce semantic parsing for task-oriented dialogue. We implement novel shift-reduce parsers that rely on Stack-Transformers. This framework allows to adequately model transition systems on the Transformer neural architecture, notably boosting shift-reduce parsing performance. Furthermore, our approach goes beyond the conventional top-down algorithm: we incorporate alternative bottom-up and in-order transition systems derived from constituency parsing into the realm of task-oriented parsing. We extensively test our approach on multiple domains from the Facebook TOP benchmark, improving over existing shift-reduce parsers and state-of-the-art sequence-to-sequence models in both high-resource and low-resource settings. We also empirically prove that the in-order algorithm substantially outperforms the commonly-used top-down strategy. Through the creation of innovative transition systems and harnessing the capabilities of a robust neural architecture, our study showcases the superiority of shift-reduce parsers over leading sequence-to-sequence methods on the main benchmark.