Why does the neutral hydrogen velocity have this characteristic behavior in the galactic plane?
The reason is detailed in depth in this pdf, which contains the following diagram:



Some key quantities:


$R_0$: Distance from the observer to the center of the Milky Way
$R$: Distance from target gas to the center of the Milky Way
$V_0$: Velocity of the observer with respect to a certain reference frame
$V$: Velocity of target gas with respect to the same reference frame
$l$: Angle between $R_0$ and $\mathbf{SM}$, the distance to the gas


When measuring the radial velocity, we look for the projection of $V$ onto our line of sight. Some geometry results in the relation
$$V_r=V_0\left(\frac{R_0}{R}-1\right)\sin l$$
for the radial velocity $V_r$, assuming $V\approx V_0$ (which is not always true!). The $\sin l$ term, in addition to the asymmetrical rotation of the Milky Way, leads to the peculiar data you asked about.