Due to the effects described in the article, entering a road that's close to congested imposes negative externalities due to the delay on everyone behind you, even higher if you are pushing the road below optimal throughput. Push that externality into the price, and suddenly drivers will change their behavior in the desired fashion:
1. People will move their travel to less expensive times. Even if no other change occurs than people waiting for prices to fall, the roads operate at much higher throughput due to never getting into the region of diminishing throughput.
2. People will carpool/vanpool/mass transit- no need for any special treatment for transit, a bus with 50+ people can simply outbid most cars on the road for space, even accounting for the difference in road space taken by the bus. With the economic incentive in place, you'd even expect private buses/etc to pop up spontaneously. Right now, its rarely worth it to pool/bus- it adds extra time for you, but the benefit to the road you never see. With proper pricing, its still faster to take a car, but a lot more expensive- and the carpool/bus/etc is still probably faster than driving would be with congested roads.
3. Similarly, the high prices will incentivize alternatives such as biking, subways, etc, and give very good information on exactly what routes are in high demand when, estimates of how much an improvement would be worth, etc.