Is it legal to add a jumper wire to a conductor that is too short in a junction box?
I think 300.14 is quite clear.  You need at least 6" of free conductor, and the conductors must be long enough to extend 3" out of the box.  If you can't pull more cable into the box, you're going to have to replace it.  

As others have mentioned, 314.17(C) requires at least 1/4" of the cable sheath to be in the box.  So the inspector might call you on that as well.