I think you lower your pitch to let the plane accelerate so I guess you should be done by 4000. But still I agree it’s a little margin. The best option would be for the PF to reduce the thrust levers as only the PF knows how much thrust he/she needs and adjust accordingly. Think about level flight, your on your way to the localiser and you have flap 5, speed 170... who holds the thrust then? What if he gives you 3000ft? 4000ft isn’t certain its minimum 2500 on that SID. Also think about in the go-around, you maintain flap 15 until level off then begin to accelerate.. the throttle is used by the PF.
A good move would be to mention that this threat may occur, the if it does happen who has which responsibilities etc.