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Warp2 effect has a 'direction' in which it creates the illusion of moving the texture. Is there any way to change it?

You need to build your own [wiki]SHADERS[/wiki], just play with values checking inside the main .pk3 file (not sure if you are using qzdoom, zdoom or gzdoom so) on \shaders\glsl\func_warp2.fp, create a folder called "shaders" and apply them on desired textures / graphics / sprites.