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10 pags., In this article, we reexamine the derivation of the dynamical equations of the Ashtekar-Olmedo-Singh black hole model in order to determine whether it is possible to construct a Hamiltonian formalism where the parameters that regulate the introduction of quantum geometry effects are treated as true constants of motion. After arguing that these parameters should capture contributions from two distinct sectors of the phase space that had been considered independent in previous analyses in the literature, we proceed to obtain the corresponding equations of motion and analyze the consequences of this more general choice. We restrict our discussion exclusively to these dynamical issues. We also investigate whether the proposed procedure can be reconciled with the results of Ashtekar, Olmedo, and Singh, at least in some appropriate limit., This work has been supported by Project. No. MICINN FIS 2017–86497-C2-2-P from Spain (with extension Project. No. MICINN PID 2020-118159GB-C41 under evaluation). The project that gave rise to these results received the support of a fellowship from “la Caixa” Foundation (ID 100010434). The fellowship code is LCF/BQ/DR19/11740028. Partial funds for open access publication have been received from CSIC