Cron has gone haywire, runs duplicate jobs

Since upgrading to WP 3.6 cron has been misbehaving. Many jobs get run dozens of times*. Presumably because the next run status does not get updated i.e; in crontrol, many jobs that have recently run still show the next run as “now.” If I manually set them to the last time they were to have properly been invoked, that value remains until they are run, at which point they become stuck in “now” (a time in the past when they were first invoked after the set next run time).

I tried disabling WordPress’ implementation of cron in my config
define( 'DISABLE_WP_CRON', true );
but still runs, and produces the same unfortunate behavior. How can I remedy this?

I’ve tried searching the forums, the site search never gives any output, and googling with site: only gives outdated topic listings.

This morning I received 160 messages (identical content, but sent separately with unique Message IDs) over the course of 4 hours from WP Better Security’s file change detection. I have also received dozens of copies of the same emailed database backup from WP-DB Manager, and my members were thrilled to receive 30 copies of the weekly site digest from Subscribe2 last Tuesday.