With the development of artifact-centric Business Process Management (BPM) models, the search for fully decentralized and less complex BPM techniques re-emerged in the last decade. In this context, the Language for the Specification of Administrative Workflow Processes (LSAWfP) and a fully decentralized execution model of its specifications have been proposed between 2019 and 2021. These new tools make it possible to specify business processes by means of a grammatical model and, to execute them in a decentralized mode via a protocol whose key algorithms (called projections) are intended to guarantee the confidential execution of certain tasks. In this paper, improvements to this execution model are proposed in order to overcome two previously formulated (disabling) assumptions. The resulting execution model allows the use of iterative routing in the specification of processes to be executed (increase of expressiveness); furthermore, the performance of the execution model's key algorithms are significantly improved while preserving properties of the original model as well as possible.