Same problem as many here, KB2919355 fails with error 8007007E.
Any help would be appreciated.
@hurleyp, there appear to be many reasons why KB2919355 is not installing. Some people have been able to recover, others have had to do an in-place repair or a re-install (both require Win 8.1 installation media) or rebuild their their systems from scratch.
For your 0x8007007E error, the following posts might be useful:
Although the first one references Windows 7 and the CheckSur tool, the link ends up at http://support.microsoft.com/kb/947821 which describes how to use the Windows 8/8.1 DISM tool.
I have run sfc /scannow, DISM.exe /Online /Cleanup-image /Restorehealth and reset the Windows Update components multiple times. In the end I had to do an in-place repair (I suspect I had a different root cause) but at least the steps did not appear to cause any further damage. Doing a clean boot is also a good idea in case some application/service is interfering with the update process.