Tumour tracking is an advanced radiotherapy technique for precise treatment of tumours subject to organ motion. In this work, we addressed crucial aspects of dose delivery for its realisation in pencil beam scanning proton therapy, exploring the momentum acceptance and global achromaticity of a Gantry beamline to perform continuous energy regulation with a standard upstream degrader. This novel approach is validated on simulation data from three geometric phantoms of increasing complexity and one liver cancer patient using 4D dose calculations. Results from a standard high-to-low beamline ramping scheme were compared to alternative energy meandering schemes including combinations with rescanning. Target coverage and dose conformity were generally well recovered with tumour tracking even though for particularly small targets, large variations are reported for the different approaches. Meandering in energy while rescanning has a positive impact on target homogeneity and similarly, hot spots outside the targets are mitigated with a relatively fast convergence rate for most tracking scenarios, halving the volume of hot spots after as little as 3 rescans. This work investigates the yet unexplored potential of having a large momentum acceptance in medical beam line, and provides an alternative to take tumour tracking with particle therapy closer to clinical translation.