This [1] solves it in 3.4212 average guesses 100% of the time and claims optimality, which is 99% of the difficulty it seems. For the limited 2671-word set of possible words, I think the question is now settled (for the whole 12k-word set, I don't think anyone tried anything).
It was posted here four days ago [2].
[1] http://sonorouschocolate.com/notes/index.php?title=The_best_...
[2] https://news.ycombinator.com/item?id=30006724