Astrophysical plasmas are often highly conducting, but finite resistivity can nevertheless influence the evolution of strongly magnetised systems. Capturing these effects in general relativistic magnetohydrodynamics is computationally challenging because high conductivity leads to stiff source terms in the evolution equations. Standard numerical approaches rely on implicit-explicit (IMEX) time integration to maintain stability, but this substantially increases the complexity and computational cost of the simulations. Building upon the previously developed Resistive Extension upGrade for Ideal MagnEtohydrodynamics (REGIME), we present a new fluid-frame formulation that simplifies the incorporation of leading-order resistive effects by avoiding matrix inversions required in previous approaches. The method is implemented in a general relativistic magnetohydrodynamics code and validated through one-dimensional current-sheet tests and simulations of isolated magnetised neutron stars and binary neutron star mergers. We find that the new formulation reproduces the expected resistive behaviour with accuracy comparable to IMEX-based methods, while substantially reducing the computational cost and complexity of the simulations. In binary neutron star mergers, finite resistivity leads to measurable differences in the post-merger gravitational-wave signal and remnant structure, showing that resistive effects can produce measurable changes in the post-merger dynamics even in the high-conductivity regime.