First, hopefully you let it go to voice mail since you’re relased until 1600.
Second, up to you — I’d likely show at 4, see what the scoop is (did whole trip get recrewed, FSB CA used too, or did FO call fatigue?), go to gate and push when you’re good and ready to safely do so.
Even if the push is late, they’re still well ahead of using a short call. And yes, they can assign the departure any time after you’re on, but they take the hit for any lates. You can ask for some add pay for on time, but up to them to give you any.