  We continue our series of papers on phase-space distributions of stars in the
Milky Way based on photometrically derived metallicities and Gaia astrometry,
with a focus on the halo-disk interface in the local volume. To exploit various
photometric databases, we develop a method of empirically calibrating synthetic
stellar spectra based on a comparison with observations of stellar sequences
and individual stars in SDSS, SMSS, and PS1, overcoming band-specific
corrections employed in our previous work. In addition, photometric zero-point
corrections are derived to provide an internally consistent photometric system
with a spatially uniform metallicity zero point. Using our phase-space
diagrams, we find a remarkably narrow sequence in the rotational velocity
($v_\phi$) versus metallicity ([Fe/H]) space for a sample of high proper-motion
stars ($>25$ mas yr$^{-1}$), which runs along Gaia Sausage/Enceladus (GSE) and
the Splash sub-structures, and is linked to the disk, spanning nearly $2$ dex
in [Fe/H]. Notably, a rapid increase of $v_\phi$ from a nearly zero net
rotation to $\sim180$ km s$^{-1}$ in a narrow metallicity interval ($-0.6 \leq$
[Fe/H] $\leq -0.4$) suggests that some of these stars emerged quickly on a
short gas-depletion time scale. Through measurements of a scale height and
length, we argue that these stars are distinct from those heated dynamically by
mergers. This chain of high proper-motion stars provides additional support for
recent findings that suggest a starburst occurred when the young Milky Way
encountered the gas-rich GSE progenitor, which eventually led to the settling
of metal-enriched gas onto the disk.

Astrophysics of Galaxies;Solar and Stellar Astrophysics