Steven Mulroy has posted this draft on SSRN (National Civic Review).  Here is the abstract:

The Department of Justice has never explicitly stated a policy regarding the appropriateness of alternative, non-district electoral systems, such as limited voting, cumulative voting, or preference voting, to remedy minority vote dilution under the Voting Rights Act, except to say that they may be appropriate in certain circumstances to correct the problem of under-representation of minorities. However, an examination of the Department’s administrative preclearance determinations, and the position taken during litigation, reveals certain patterns in Department treatment of these issues. Specifically, the Department supports the use of such systems, provided that the minority group is sufficiently numerous to make use of them, and provided that a sufficiently ambitious voter education program is used to ensure that voters understand them.