Sorry man wish I could help you out more but since I have never had this issue myself, I can't interject any kind of help other than sharing a link to autoprimes Backup_EFS_Final.zip, http://downloads.codefi.re/autoprime/LG/LG_G2
, thought it might help you out (there's a lot of other good stuff there too) but again never faced this issue with my G2 so best of luck with it bro!
Also just curious in your OP, you say you tried flashing a custom recovery, what custom recovery/version are you trying to use? Have you had this recovery on the phone previously? I have found this phone is VERY picky with accepting custom recoveries!
Phone: Sprint LGE G2 LS980
Custom Recovery: TWRP 22.214.171.124
ROM: Stock Jellybean 4.2.2
Carrier: Simple Mobile
LG G2 Index of ROMS, Kernels, and more!!! HERE