Its worth noting here that for starters I wouldnt use a cone just use a long cylinder with a focal length on the camera of say 22 to start with and go lower if you need to. Sometimes a forced perspective with objects can counter act the illusion so just go with a proper tunnel, the low Focal setting will help put more perspective on it.

Displacement maps are not great for distorting generally, you are essentially putting a 2d image and bending/twisting so its going to have an adverse effect on its the objects uv and final look. Also the jagged edges on the render will look like this the closer you go especially with that low amount of polys on the mesh, Increasing the amount of polys will help smooth it out.

There are ways to set up animated displacements but they are hard to control because you will get a swim effect because of the afore mentioned distorting of the mesh. Its not uncommon to 'drive' dis maps on character facial expressions but its still hard to do, again it all swims. This is the reason Dis maps were not used on the Characters in Avatar. Facial stuff was all 'in mesh'

The Approx node will help raise the displacement or lower it, and you can also make the distortion finer by using the spatial setting. with say 3 min 5 max to begin with, and length on 0.001

cheers
Jay