Vertical pressure gradient fields of supercells get very complex, particularly for non-ideal shear profiles. There are both linear and nonlinear forcings - and it is tough to make a general model so often special case scenarios are developed (e.g., straight-line, quarter turn, half circle and full circle hodographs). Mike is drifting around the linear forcing side - which as previously discussed you can get a buildup of air on the upshear side of the storm and subsequent relative high pressure aloft (so linear forcing is interaction between the updraft and the environmental shear) in the case of a straightline hodograph. More typically, the hodograph veers with height, which rotates the high and low couplet aloft clockwise (with the 'low' now on the south side, this favors rightward storm propagation). The problem with the RFD arising from the downward perturbation pressure gradient is that if air is forced to the surface from mid-levels - it would be hot and dry by the time it made it to the ground. What is observed, however, among the storms favorable for strong and long-lasting tornadoes is that the RFD is warm and moist, and more typically cold and moist in most nontornadic supercells. So, this makes the paradigm of air sinking from mid-levels inconsistent. What appears more likely is that the colder the air in the RFD, the higher it's origins with cooling largely from evaporation of rain, and warm RFD's are probably originating from a much shallower height.
Glen