We present a modification of the vacuum filtration technique for fabricating transparent conductive SWNT thin films with local nematic-like orientational ordering. Dilute SWNT surfactant dispersions are filtered through a vacuum filtration setup in a slow and controlled fashion. The slow filtration creates a region of high SWNT concentration close to the filter membrane. While slowly moving through this region, SWNTs interact and align with each other, resulting in the formation of thin films with local nematic ordering. Scanning electron microscopy and image analysis revealed a local scalar order parameter (S-2D) of 0.7-0.8 for slow filtration, three times higher than those produced from "fast filtration" (S-2D approximate to 0.24). Orientational ordering is demonstrated with different stabilizing surfactants, as well as with dispersions enriched in metallic SWNTs, produced by density-gradient ultracentrifugation. Simple estimates of relative convective versus diffusive transport highlight the main differences between slow versus fast filtration and the resulting SWNT concentration profiles. Comparisons with previous studies on three stages of liquid-crystal phase transition provide insight into the spontaneous ordering process, indicating the lack of a "healing stage", which results in a microstructure consisting of staggered domains in our SWNT films.