Send Morel down, yes.
But maybe not stop there -- send Beckham down too, let him get his swing and confidence back. How is Lillibridge at 2B? I seem to recall that IF is his original position -- maybe plug him in at 2B and put Vizquel at 3B and, dare I say, let Teahen spell him on occasion. At least shore up the defense so that the starting pitching, which hasn't been all that bad, might win them a few 2-1, 3-2 squeakers until the offense wakes up (and the offense WILL wake up -- hopefully before the Sox have buried themselves further in the standings).
Regardless, some kind of shake-up is in order here....