We have recently demonstrated how potential energy surface (PES) interpolation methods, such as kernel ridge regression (KRR), can be combined with accurate wave function time-propagation methods, specifically the multiconfiguration time-dependent Hartree (MCTDH) method, to generate a new "on-the-fly" MCTDH scheme (DD-MCTDH) that does not require the pre-fitting of the PES, which is normally required by MCTDH. Specifically, we have shown how our DD-MCTDH strategy can be used to model non-adiabatic dynamics in a 4-mode/2-state model of pyrazine, with ab initio electronic structure calculations performed directly during propagation, requiring around 100 h of computer wall-time. In this Article, we show how the efficiency and accuracy of DD-MCTDH can be dramatically improved further still by (i) using systematic tensor decompositions of the KRR PES, and (ii) using a novel scheme for diabatization within the framework of configuration interaction (CI) methods which only requires local adiabatic electronic states, rather than non-adiabatic coupling matrix elements. The result of these improvements is that our latest version of DD-MCTDH can perform a 12-mode/2-state simulation of pyrazine, with PES evaluations at CAS level, in just 29-90 h on a standard desktop computer; this work therefore represents an enormous step towards direct quantum dynamics with MCTDH.