Why would CaSO4+K3PO4 not result in a precipitate reaction? I Keep coming up with CaPO4 and KSO4 as the product, which should both form precipitates. Is it because they are both solids to start?

Check the formulas of your products - they are VERY incorrect. I would assume that the solid reactant compounds would be dissolved in water to conduct the reaction. One of the products is insoluble in water, the other is water soluble. You will have to figure which is which.