Understanding the heliospheric modulation of galactic cosmic rays is essential for studying the acceleration and propagation processes of these particles, as well as for establishing models of radiation exposure and associated risks in space missions. In this work, we build upon a previously developed long-term GCR forecasting tool and present our efforts to improve it by incorporating additional datasets and refined modeling details. The model is based on a numerical description of the transport mechanisms of charged particles in heliospheric turbulence and their relation to solar activity. In particular, we extend the cosmic-ray dataset to include monthly carbon fluxes from the ACE mission, time-resolved PAMELA proton flux and the latest high-precision AMS-02 nuclei measurements, relating them to solar activity proxies. Utilizing multi-channel fitting provides new opportunities to investigate correlations between cosmic-ray fluxes and solar proxies across different solar cycle phases, and point toward possible advances in long-term forecasting capabilities.