One additional item springs to mind: they need to compel ALL public companies to register stock and to report.
Perhaps it would be possible to devise simpler filings for small companies that would be less expensive to compile. They might also experiment with making templates for those filings: the company would simply fill in the blanks, rather as one does with tax returns. Certain matters might have to be explained in appendices.
But the benefit would be that they'd be automatically searchable; they could be set up to trigger alerts in specific circumstances, and the computer could also automatically compare entries to earlier filings.
Two missed filings and registration would be revoked until those filings are completed.
And speaking of that, they could do a better job of revoking the registration of companies that are reporting but haven't filed in years. They're working on it, little by little, but I see no reason why they couldn't speed it up.
For the automated filings, they'd need some sophisticated programming, but it's available: