Sum-frequency generation enhanced by electromagnetically induced transparency (EIT) has been extended to the production of extreme ultraviolet (XUV) radiation in the range 97.3--92.6 nm from $np\ensuremath{-}1s$ transitions $(n=4--8)$ in atomic hydrogen. Pulsed radiation was generated by strong coupling of the $\mathrm{np}$ and $2s$ levels with laser radiation at Balmer wavelengths, and simultaneously (weaker) coupling of the $2s$ and $1s$ levels by two-photon resonance with 243-nm laser radiation. Investigations were carried out over a range of laser intensities and products of interaction length and atomic density $(\mathrm{NL}).$ As the product $\mathrm{NL}$ increased, the XUV intensities were greatly enhanced by EIT, and at high $\mathrm{NL}$ values, the spectral distributions of some of the generated signals were found to be distorted by the presence of molecular hydrogen. Calculated profiles, modified to incorporate the effects of nearby molecular resonances, were shown to be in good agreement with the observed spectra.