  We demonstrate a velocity selection scheme that mitigates suppression of
electromagnetically induced transparency (EIT) by Doppler shifts for low--high
EIT probe--coupling wavelength ordering. An optical pumping beam
counter-propagating with the EIT probe beam transfers atoms between hyperfine
states in a velocity selective fashion. Measurement of the transmitted probe
beam synchronous with chopping of the optical pumping beam enables a
Doppler-free EIT signal to be detected. Transition frequencies between
5P$_{1/2}$ and $n$S$_{1/2}$ states for $n=$26, 27, and 28 in $^{39}$K are
obtained via EIT spectroscopy in a heated vapor cell with a probe beam
stabilized to the 4S$_{1/2}\rightarrow$5P$_{1/2}$ transition. Using previous
high-resolution measurements of the 4S$_{1/2}\rightarrow$nS$_{1/2}$
transitions, we make a determination of the absolute frequency of the
4S$_{1/2}\rightarrow$5P$_{1/2}$ transition. Our measurement is shifted by 560
MHz from the currently accepted value with a two-fold improvement in
uncertainty. These measurements will enable novel experiments with
Rydberg-dressed ultracold Fermi gases composed of $^{40}$K atoms.
