Craig
I have a few steps that I try to do in order... My shop has bad arc blow for SMAW, but the direction of the blow differs from day to day so the solutions do also.
1. Work clamp close to weld... Weld away from clamp.
2. Wrap work cable clockwise around table leg or pipe if possible. weld away from clamp
3. Wrap work cable counterclockwise around leg or pipe,,, Weld away from clamp
4. Repeat steps welding toward clamp (this is a last resort and doesn't often work)
There is a difference between thermal arc blow and magnetic arc blow. The first thing you need to is identify which is your case.
You've stated it's thermal arc blow, but then you've stated "I've tried turning down the heat and moving the ground clamp w/ no success"
That later sentence implies you suspect magnetic arc blow rather than thermal arc blow. I believe the other responses reflect that implication.
With that said, let's give a rough definition of the two most common forms in ascending order of probability.
Thermal arc blow: As you advance along the plate, the gap between the rod and the surface of the weld pool is ionized. That space becomes more conductive and facilitates transfer of the arc/heat from the rod to the plate. This condition sets up "thermal back blow" as the arc attempts to maintain itself through the ionized hot space rather than the cold space/cold plate. Some level of thermal back blow is not detrimental and effectively unavoidable. However; when you try to run to fast, or without enough heat, you're trying to transfer the arc through a zone of higher resistance with the inherent weld quality issues that evolve from that condition.
Magnetic arc blow: MAB is due to magnetic lines of force/eddys in an unbalanced condition. It is also the reason thermal arc blow (TAB) is hard to diagnose. The inherent pushing of the arc due to magnetic lines of force/flux can push the arc away from the ionization zone and into a more resistive area which by default increases the arc blow effect. Going back to what causes MAB when those lines of force get out of balance, they tend to leave every increasing levels of residual magnetism. In effect the situation just makes itself worse the longer it's left unaddressed. After some time, TAB is no longer a concern.
Fixing MAB is relatively straightforward in that you either eliminate residual magnetism, and or balance the magnetic flux conditions. You've already received some valuable comments in that regards. Defining the difference between TAB and MAB and in particular, the point in which one begins to amplify the other, that is not so easy.
Some additional information;
Most articles I've read claim MAB can only be caused by 50 gauss (as determined by gauss's law for magnetism) but the evidence I've personally witnessed and researched defies that common logic in that it does not take into account the lower levels in which < 50 gauss flux lines amplify the inherent effects of TAB without leaving > 50 gauss in residual magnetic flux lines. It also doesn't take into account the materials in question. Nickel in particular is also ferromagnetic with a low curie temperature. That low curie temperature when welding materials high in Ni, causes the magnetic domains to align and snap the moment the metal drops below the curie temp. Unlike Fe which has a high curie point, the lower curie point of Ni effectively gives more time for alignment of the magnetic domain fields.
These are just some of the points to be considered. I'll desist on theory at this point. But I do strongly suggest you identify which is your case (TAB or MAB) before proceeding.
Regards,
Gerald
Craig, I've expirienced similar stuff and found the problem in my shop was that over time running multiple welders through their various levels of qualification testing all in the same weld test booth, the table and fixture developed residual magnatisim (noticed by the grinding dust accumulating like metalic fuz on tool that were left on the welding table). 
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