[Last updated: 1 May 2016]
Apparently, the Aquos Crystal 306SH and the Aquos Zeta SH-01G can be rooted now, thanks to tewilove.
However, the app requires a passcode to use, which tewilove asks a fee for, but has failed to reply to my requests to purchase a code, and to other people's as well.
You can find out more about the 306SH in the dedicated forum on XDA Developers: http://forum.xda-developers.com/aquos-crystal/general
The app that roots the SH-01G is only available on Chinese Baidu forums (can be downloaded by anyone) but still requires a passcode to use.
Here is a link to the latest version that supposedly roots build versions 01.00.08 to 02.00.02: http://tieba.baidu.com/p/4470982444
My SH-01G has build version 01.00.07, so I cannot test this app. All earlier versions (that I was able to install) have failed to accomplish anything.
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