Alternative approach: create a new moderator class (Garbage collectors) accessible at a lower rep (2-3k) that has the full range of 10k moderator options only for questions older than 30 days with score <= 0 and no accepted answer.

Alternative approach: create a set of "Garbage Collector" tools for people with rep>=3k that shows which questions have active close votes so that other people can find them and help close them within the 4-day window if they think that's appropriate. Maybe it would just be another tab on the main page for people who have the necessary rep. Being able to see questions by new users might also be helpful so that questions that need to be migrated an be found and moved quickly.