The more I think about it, if the coolant is not terribly hot, but the fan is cycling on and off, I would almost bet money there is a compression leak at the head gasket. Cylinder pressure is leaking in to the cooling system. I'll bet it runs ok with the radiator cap off but spews out coolant with the cap on.
I had that situation with mine. Rebuilt the engine, overheated it, determined I had blown the head gasket, replaced the head gasket again, had bubbles in the coolant, determined I had not bled it correctly and overheated again, replaced head gasket again. No bubbles, no problem....