Seen just outside the innermost regions of the galactic center, the kinematics of molecular gas are dominated by a handful of compact but unusually broad-lined features of enigmatic origin. We show, using previous data, that there is a family of such features whose members are distinguished morphologically by their extreme vertical extension, perpendicular to the inclined plane of the overall gas tilt. Having isolated the features spatially, we mapped them with varying degrees of completeness at high resolution (1') in lines of 12CO, 13CO and CS. Although very broad profiles exist in some individual beams, more generally we resolved the kinematics into spatial gradients which earlier were smeared in broader beams to form wider lines. The largest apparent velocity gradients are typically with respect to galactic latitude but motions are confined to the range of velocities inside the galactic terminal velocity, indicating that it is the galactic gravitational potential which is being tapped to create the observed kinematics. We interpret the broad-lined features qualitatively in terms of recent hydrodynamical models of gas flow in strongly barred galaxies: standing shocks which occur where gas enters the Galactic dust lane can account for the presence of broad lines over small spatial volumes wherever molecular gas is actually engaged in this process. To interpret the dynamical sequencing of the complex behaviour seen within the broad-line features we discuss how the Sun must be oriented with respect to the bar. In doing so, we identify the nuclear star-forming rings seen in other galaxies with the complex of giant H II regions Sgr A, B, C etc. and show that the kinematics are as expected for a ring of radius 175pc (for a Sun-center distance of 8.5kpc) rotating at about 210km/s. Gas having clear and strong outward-directed non-circular motion around l=0° (the famous ``expanding molecular ring'') is then associated with the ``spray'' of incoming gas at the inner ends of the dust lane, defining a more nearly end-on viewing angle for the bar. Using the inferred geometry, we construct a narrative for the behaviour of the feature most completely mapped here, at l=5.4°, whereby gas basically falls out of the sky and is concentrated into the observed dense, bright molecular core before being shredded and sucked into the inflow of the dust lane 100pc or more below the nominal galactic equator. From there it is recycled and lifted back into the more nearly equatorial region of the nuclear ring. Of course, the vertical structure of this and the other features, and the overall tilt of the dust lane and inner-galaxy gas layer, all remain to be discussed theoretically.