Gate-modulated transport through partially aligned films of single-walled carbon nanotubes (SWNTs) in thin film type transistor structures are studied experimentally and theoretically. Measurements are reported on SWNTs grown by chemical vapor deposition with systematically varying degrees of alignment and coverage in transistors with a range of channel lengths and orientations perpendicular and parallel to the direction of alignment. A first principles stick-percolation-based transport model provides a simple, yet quantitative framework to interpret the sometimes counterintuitive transport parameters measured in these devices. The results highlight, for example, the dramatic influence of small degrees of SWNT misalignment on transistor performance and imply that coverage and alignment are correlated phenomena and therefore should be simultaneously optimized. The transport characteristics reflect heterogeneity in the underlying anisotropic metal-semiconductor stick-percolating network and cannot be reproduced by classical transport models.