Ok I thought up another way around your problem. Put this zip on the root of your internal storage and rename it update.zip. Next reboot into recovery (CWM or TWRP) and install the zip from there and reboot. It should then reinstall the apk during boot up.
http://filetrip.net/dl?s6J6Aojrs7 Try this instead, should lead to the download page instead of the embedded one.
Okay. Next problem. This is what appears when I boot into recovery mode: