The aliasing you see is a limitation of logarithmic depth buffer based in the EXT_frag_depthWebGL extension. It is not fixable unless you use software emulation or a complete different approach like reverse depth buffer (which is not yet supported in three.js).
So we have gone for the option you have suggested - i.e. force three.js to emulate logarithmic depth buffer in software. The approach has a few downsides, but I think for now it is the best option. Below we list the downsides, just in case others are dealing with the same issue.
Second, the software emulator does some strange things (is it the front clipping plane?). For now, we decided just to live with it and see what happens… Below are a couple of images to show the issue.
Third, even when using the software emulator, we still get some depth issues at certain camera rotations. But it is much less pronounced. Again… we just decided to live with it for now. The image below shows the issue. The grid lines should not be showing through the polygon that defines the base.
Fourth, performance-wise, we are not really sure what impact it has.