A lottery is such an obvious solution that we can only conclude that the people who developed the Harvard admission process are irredeemable racists.
The data is pretty shocking and closely guarded by the testing people who believe they'd be asked to shut down altogether if it got out.
[1] https://i0.wp.com/www.brookings.edu/wp-content/uploads/2017/...
Such an approach will likely encourage diversity as people who think they don't have a chance under the current system will apply.