Context. Imaging atmospheric Cherenkov telescopes (IACTs) are used to observe very high-energy photons from the ground. Gamma rays are indirectly detected through the Cherenkov light emitted by the air showers they induce. The new generation of experiments, in particular the Cherenkov Telescope Array Observatory (CTAO), sets ambitious goals for discoveries of new gamma-ray sources and precise measurements of the already discovered ones. To achieve these goals, both hardware and data analysis must employ cuttingedge techniques. This also applies to the LST-1, the first IACT built for the CTAO, which is currently taking data on the Canary island of La Palma. Aims. This paper introduces a new event reconstruction technique for IACT data, aiming to improve the image reconstruction quality and the discrimination between the signal and the background from misidentified hadrons and electrons. Methods. The technique models the development of the extensive air shower signal, recorded as a waveform per pixel, seen by CTAO telescopes' cameras. Model parameters are subsequently passed to random forest regressors and classifiers to extract information on the primary particle. Results. The new reconstruction was applied to simulated data and to data from observations of the Crab Nebula performed by the LST-1. The event reconstruction method presented here shows promising performance improvements. The angular and energy resolution, and the sensitivity, are improved by 10 to 20% over most of the energy range. At low energy, improvements reach up to 22%, 47%, and 50%, respectively. A future extension of the method to stereoscopic analysis for telescope arrays will be the next important step.