You might want to try those self-threading needles, the ones with the slot on the top.
Put your needle in (without any thread in it) right at the base of the thread to be tied off, make it come out more than an inch away (without going all the way through the quilt and showing on the other side). Then snap the short thread into the needle eye and pull it through. The thread will go into the quilt and not be long enough to come out the other end.