Floor press could help. I would also suggest setting the pins or safeties or whatever you have right where you usually start failing. Set the barbell on it and start your reps from that position. Pause each rep on the safeties use a tight positioning and explode
Floor presses might help a little, they help the seond half of the lift.
Have you considered some speed work? (50-60% 1RM, 2-3 reps as fast as possible, 8-10 sets with 45-60 secs rest) The faster you can get the bar off of your chest, the easier the lift will be.