I've worked in a Little League with similar setups for the past several years. The home scorekeeper is official, and the electronic scoreboards are rarely used. I agree with you that you're not likely to reconstruct the second inning at the end of a game, and it sounds like you handled a crappy situation pretty well.
FWIW, I typically ask the scorekeepers to check with each other twice: once at the third inning, once after the next-to-last inning (eg, after the fifth for a six-inning game). I don't want to know the score; I just want to know that they agree. If there is a scoreboard, I might ask them if they agree with the board at the same inning markers.
I also confirm any potential score/no-score decisions at the end of an inning with both books immediately.
Good luck avoiding this in the future!
