It looks like you almost figured it out, your bottom-most Color Ramp controls the amount of white nicely:
The problem is, the plane is still not filled with white when the white slider moves all the way to the left. This is because a Color Ramp expects an input in range $0…1$, so anything below $0$ is clamped to (becomes) $0$, and everything above $1$ is clamped to $1$. Meanwhile, some Heights are below $0$…
The general solution is to find out what's the minimum possible value that can go to the color ramp, what's the maximum possible value, and use a Map Range node to normalize that range (convert to $0…1$):
The GIF size limit forces grotesque inaccuracy but the idea is you can also increase the scale and play with the parameters that are expected to change to discover what are the minima and maxima (you could read the documentation instead, but don't trust the docs too much…). And more importantly, you can often add some safety margin and increase/decrease the maximum/minimum some more.
However, in your case you're not going to animate the movement of Color Ramp slider, so you would need to alter the input to the Color Ramp. and with that, you don't need to map range:
But in this case, the Color Ramp is not needed:
Gradient across $y$ axis
To modify the threshold based on $y$ axis instead of $t$ axis… Simply plug the $y$ coordinate instead of time. I added an additional Math: Multiply Add node to further offset the gradient to your liking (add) and control the height of the gradient (multiply):