well, i only know a little about palms, and am not sure exactly what kind of palm you are talking about... but...
when any
plant needs moved, the best way is to disturb the root system as little as possible.
if the palm is like most, the roots will be slightly smaller in diameter than the drip line of the
tree, IF that big. what i would do, is dig around the drip line (the fartherest edge of the fronds) and try to "scoop" the
tree. now, this sounds like a problem, but, if you do one side, then put down a sheet/tarp/blanket, and then start on the other side, it can be tilted over onto the blanket with the dirt still in place around the roots (so as not to disturb them). then, using the blanket, you can lift or drag the
tree to its new, prefered home.
now that the mechanics are there, the best time to move a
tree is when it is about to go dormant (up top) so that the roots can develope. for you, that will either be now, when the moisture is about to "dry up" forcing the roots to spread farther looking for water, or, at the end of your summer, before it starts to get cold.
the advantage to moving it now is that it won't get any bigger before you move it, and you can monitor its progress and give it extra drinks if need be. good luck and let us know how you make out!