Changes in periods of Miras is a very active field of research as it might shed further light on stellar evolution in the Asymptotic Giant Branch (AGB) of the HR diagramme. One popular view is that period decrease is due to contraction during the initial stage of the thermal pulse in the helium burning shell, as you indicate.
Another period changer is T UMi. Coincidently there is an MRAS pre-print on ArXiv only today on “Hydrodynamic modelling of pulsation period decrease in the Mira-type variable T UMi” which pursues the matter. It considers hydrodynamic models and non–linear stellar pulsations. The references therein are worth following: https://arxiv.org/abs/2206.08360
Keeping up with ideas and literature in this area could be a fulltime job, but we are lucky to have the monthly AGB Newsletter to help us as it summarises recent literature. You can subscribed to it here: https://www.astro.keele.ac.uk/AGBnews/
The June edition is the 299th, and celebrations are promised for the July edition. It is available here: https://www.astro.keele.ac.uk/AGBnews/issues/AGB299.pdf
The last chapter on this fascinating topic has yet to be written! But it is interesting to note that the research, and the associated models, depend on amateur observations of Miras over many years.