Better than lengthening the yellow -- create one second of 4-way red between cycles. It gives an opportunity for all cars to clear the intersection before the next green.
Yep. That is the way to do it. People just get used to a longer yellow and push the envelope to match.
'Course, once they figured out what was going on with the delayed green after the light turned red, they'd just push that. I would. But then, I don't run red lights unless it is VERY obvious that nobody is coming.