In the second part of our series on integrated photonic spectrographs for astronomy, we present theoretical and experimental results on the design, simulation and characterization of custom-manufactured silica-on-silicon arrayed waveguide gratings (AWGs) constructed using the three-stigmatic-point method. We derive several mid-to-high resolution field-flattened AWG designs, targeting resolving powers of 11,000 - 35,000 in the astronomical H-band, by iterative computation of differential coefficients of the optical path function. We use numerical simulations to study the imaging properties of the designs in a wide wavelength range between 1500 nm and 1680 nm. We theoretically discuss the design-specific degradation of spectral resolving power at far-off-centre wavelengths and suggest possible solutions. In the experimental section, we provide characterization results of seven manufactured AWG devices of varying free spectral range and resolution. We obtain estimates on spectral resolving powers of up to 27,600 for polarized input at 1550 nm from measurements of the channel transmission bandwidth. Furthermore, we numerically predict expected resolving powers of up to 36,000 in the polarized mode and up to 24,000 in the unpolarized mode for direct continuous imaging of the spectrum.