Persist is good, here. Has performed well, and the cows will eat it - some of the others I'd planted in the past - Benchmark, Potomac, etc., were the absolute last thing the cows would touch, when grazing.
I've never really planted it in any manner other than drilling it in with a no-till drill - but will be broadcasting some leftover Persist over a couple of paddocks with very thin, recently grazed stands of grass - along with some timothy & red clover - in the next week or so, just before the cows come back through, to trample the seed in.
Broadcasting over a fairly decent stand of grasses, after greenup, with no treading in would likely be a waste of seed/$$ - I'd think very little would have a shot at making soil contact and having a chance to germinate, much less the seedlings having a chance to compete with established grasses.