727 Build for Mid-10s

My rear clutch drum/input shaft assembly has about .020" of play and found this nifty video:



Since mine has the early thinner '834' clutch piston and associated diaphragm spring, is it worth upgrading to the later thicker piston and stronger later-style diaphragm spring to help minimize this play? How much slop in that assembly is too much? Is there any other way to reduce this slop other than replacing the piston?