The trans lube you smeared on the clutch plates can take up a whole lot more space than you might think. You should be installing the discs and steels dry and checking the clearance with a feeler gauge and adjusting it accordingly with the selective snap ring that gives you the proper clearance. Personally I like to see .075-.080" with a 5 disc setup checked dry. Then you pull the discs back out and soak them in ATF and reassemble it.
It's possible you have one of the thickest selective snap rings. Combine that with the assy. lube and there's your zero clearance.