Short answer is - look at Half Life 2 water for example (I know it isn't recent example, but most current days games use either cube maps or screen-space reflections, plus HL2 water has the exact same issue visible). From here you can deduce, that it's mostly ignored as the players won't notice the effect that much.
Long answer is - the petrubation is problem, as you're performing it in screen-space, you basically just offset the texture that doesn't have the info you want. One possible solution would be to store the distance of the y-flipped world from clipping plane and weight petrubation based upon this distance (clamped of course) - this might work - but I haven't tried it yet, so it might look weird. The other possible solution is to move clip-plane upwards, but this results in other artifacts.