I am a little lost on why you would be surprised that a 80's geothermal technology cannot keep up. You are in a very hot climate and would have lowest costs and best comfort with a modern SEER 12 or better AC unit. In your climate, you are probably seeing as good a performance out of a heat pump as you can reasonably expect.
To relieve load on the existing unit consider increasing attic insulation to R-38 minimum, improve attic ventilation (add powered fan), check floor insulation and go to R-13 minimum.
I think your best bet would be to get out of the ground and replace the AC with a new high Seer efficient unit.