It's perhaps useful to note that IL used a similar method for over 100 years to elect its House until it was eliminated in 1980. The state was divided into 59 three-member districts. Voters could cast 3 votes for either 1, 2 or 3 candidates dividing their votes evenly (eg. if a voter only selected two candidates they each got 1 1/2 votes). Parties ran only two candidates in a district to avoid being knocked out by strategic voting, so districts had representation from both parties.
Even in, say, inner-city Chicago would the Dems only put up 2 candidates?