Is it overheating so much it pushes water out? or just getting hot according to the gauge? Have you double checked the gauge accuracy? Just how hot is it getting? Use a hand held infra-red gun if you can find one local, check the block, head, and thermostat housing, comparing the readings to the radiator tanks and core.
Most new engines, if built right, will run hot till they get some miles on it. Was it broke in correctly? does it have some highway miles on to seat the rings? is the timing and vacuum lines correct? is the vacuum advance working?
What about the fan clearance to the radiator, as stated above 1/2" or less with stock fans and stock idle rpm. A modern big blade fan can stand to be a little ways back from the core.
Desert Cooler radiators, are they copper 4 cores? or aluminum? Aluminum will be much more efficient and should have no problem cooling anything behind it. Some of the four core radiators have so many fins that they require a lot more air flow just to get through the core. Is yours a tight fin unit or can you see through?
Add a overflow tank or bottle so any coolant pushed out will be drawn back in once it cools down, this assuming you have a overflow tube and correct cap. If there is air trapped in the engine, the overflow should take care of it after a few cycles.
What about your cap? A new radiator will handle 14psi caps just fine, old stock units should stay under 5 or 7 depending on condition. My new aluminum radiator came with a 14 psi cap!
If you are not sure if you have all the air out, pull the thermostat out and push it open and stick a aspirin in it to hold it open. The pill will dissolve after you start filling the coolant back up, but not until all the air is out.
Typical coolant problems are cause by air flow at idle speeds and poor condition radiators at driving speeds, assuming the engine tune is correct.
Joe