Full-waveform inversion (FWI) of cross-borehole Ground Penetrating Radar (GPR) data is a technique with the potential to investigate the subsurface structures. Typical FWI applications transform the 3D measurements into a 2D domain via an asymptotic 3D to 2D data transformation, widely known as a Bleistein filter. Despite the broad use of such a transformation, it requires some assumptions that make it prone to errors. Although the existence of the errors is known, previous studies have failed to quantify the inaccuracies introduced on permittivity and electrical conductivity estimation. Based on a comparison of 3D and 2D modeling, errors could reach up to 30% of the original amplitudes in layered structures with high contrast zones. These inaccuracies can significantly affect the performance of the crosshole GPR FWI in estimating permittivity and especially electrical conductivity. We addressed these potential inaccuracies by introducing a novel 2.5D crosshole GPR FWI that utilizes a 3D finite-difference time-domain forward solver (gprMax3D). This allows us to model GPR data in 3D, while carrying out FWI in the 2D plane. Synthetic results showed that 2.5D crosshole GPR FWI outperformed the 2D FWI by achieving higher resolution and lower average errors for permittivity and conductivity models. The average model errors in the whole domain were reduced by around 2% for both permittivity and conductivity, while zone-specific errors in high contrast layers were reduced by about 20%. We verified our approach using crosshole 2.5D FWI measured data, and the results showed good agreement with previous 2D FWI results and geological studies. Moreover, we analyzed various approaches and found an adequate trade-off between computational complexity and accuracy of the results, i.e. reducing the computational effort whilst maintaining the superior performance of our 2.5D FWI scheme.