It would help if you can post a screenshot or two, it is difficult to imagine what "eye bleedingly sharp" means, although the most likely possibility is overdone edge sharpening.
X264 can be achieved from Adobe CS6 in several ways. One is to install X264VFW, browse to Microsoft AVI in CS6 and what it will output is an X264 AVI. You can then extract the .264 stream. (e.g. from the Streams Extractor tool in MeGUI)
Another powerful option (and my preferred option) is to use Debugmode FrameServer in conjunction with the X264 encoder (or GUI of your choice). As the name suggests, it serves or streams frames directly into the encoder, so effectively you get X264 straight from CS6 without an intermediate.
Note that the above two methods are only available on the Windows version.
Of course, you can always render out to uncompressed and then encode an X264 file from your preferred encoder GUI. While inefficient, this is probably the easiest option. In terms of encoder GUIs, MeGUI is the most powerful and configurable. Hybrid is a great option too, and multiplatform, so the best choice for OS X (although the encoder libraries are usually a month behind Linux and Windows). Be sure to use the --bluray-compat string for X264 meant for blu-rays.