We present a large sample of 2.5-38{mu}m galaxy spectra drawn from a cross-archival comparison in the AKARI-Spitzer Extragalactic Spectral Survey, and investigate a subset of 113 star-forming galaxies with prominent polycyclic aromatic hydrocarbon (PAH) emission spanning a wide range of star formation properties. With AKARI's extended 2.5-5{mu}m wavelength coverage, we self-consistently model for the first time all PAH emission bands using a modified version of PAHfit. We find L_PAH3.3_/L_IR_~0.1%, and the 3.3{mu}m PAH feature contributes ~1.5%-3% to the total PAH power-somewhat less than earlier dust models have assumed. We establish a calibration between 3.3{mu}m PAH emission and star formation rate, but also find regimes where it loses reliability, including at high luminosity and low metallicity. The 3.4{mu}m aliphatic emission and a broad plateau feature centered at 3.47{mu}m are also modeled. As the PAH feature with the shortest wavelength, the one at 3.3{mu}m is susceptible to attenuation, leading to differences of a factor of ~3 in the inferred star formation rate at high obscuration with different assumed attenuation geometries. Surprisingly, L_PAH3.3_/L_{Sigma}PAH_ shows no sign of decline at high luminosities, and the low-metallicity dwarf galaxy II Zw 40 exhibits an unusually strong 3.3{mu}m band; both results suggest either that the smallest PAHs are better able to survive under intense radiation fields than presumed, or that PAH emission is shifted to shorter wavelengths in intense and high-energy radiation environments. A photometric surrogate for 3.3{mu}m PAH luminosity using JWST/NIRCam is provided and found to be highly reliable at low redshift.