For what it is worth, I was able to cross compile the version of cgminer found here, https://github.com/bitmaintech/cgminer, for the Beagle Board Black they use as the controller. That version has some commits after the October 3rd date of the latest S4 firmware and I was hoping for the changes CK was talking about earlier in the thread. This has seemed to address the issues with eligius for me and the S4 is averaging 2119.47 GH/s over the course of 9h 55m 26s.

http://i.imgur.com/lTACuIf.png