Yeah, that's the sketchiest and least thought-out part of it, to be sure. But my vague notion was that something like an STV system would change the dynamics of what it would take to achieve minority representation in accordance with the VRA.
I don't think that STV works here. Consider that the black population is about 15% of IL, and they are sufficiently concentrated to get 3 of 18 seats when the state is gerrymandered, and certainly should have the opportunity to elect at least 2 of 18 reps. Cook plus a couple of adjacent counties is 9 reps (eg. Lake and Kane) and it would be easy to divide that into three districts of three reps each with one at 51% BVAP and one at 36% HVAP. Then an STV could work in those districts, but a district with 3 reps and 15% BVAP would be unlikely to elect a minority candidate of choice with STV.