Job queues are deceptively tricky

You solve this simply with two cron jobs, one for weekend and one weekdays.

I find it very annoying when queue problems break into queue-of-queue patterns like in the `wait`scenario

I haven't modeled it, but I wonder how far you'd get on randomizing the policy choice for concurrency limit 1. Maybe weighted by past results, but bounded to allow it to shift instead of falling permanently into a basin.