For what it's worth I'm not sure if the firmware is necessarily to blame here - I have zero PS4 lag on any firmware (Asus or Merlin's) with NAT acceleration on over WiFi even.
You most likely have a good ISP, as for me I know mine is not great so I see things way before you would or never would notice .
But I had now 2 of these 87's and a friend that lives in my town with the same ISP has the same issue , I put dd Wrt on and no problems at all , on both .
So conclusion is the obvious , asus firmware .