I also concur with mandated opinion drafts if such is possible. I inquired about legal ways to address this matter with the Chief Justice and haven't recieved a response. Since the Justices have been invited to testify here I would like it if they may also opine on this matter as well.
Sorry, I think I must have missed that. One idea could be re-confirmation hearings if a member of the Court fails to attach their name to an opinion twice without explanation, as unlike re-confirmations relating to fixed term lengths it would have less of a political aspect, and would likely be an effective method of requiring participation from every member of the Court.
This proposal becomes significantly less feasible if we are to expand the size of the Court, however, working under the assumption that people will be less inclined to participate if one of the other, say, four Justices can do their questioning and/or discussion for them. I remain convinced that the reason for stagnation in the Court's activity is a simple lack of lawsuits in the last several years rather than any inherent flaws within the judicial system.