If you have replaced warn bits (bearings, diff copper shims and fibre washers, dog clutches), assembled parts in the correct orientation, torqued crush tube correctly, and spline sets and teeth are minimally worn then there should be no more backlash than 'normal'.
Can you clarify the bit about fitting the PTO drive?
How was the housing slightly different?
Hard to tell from videos, but front shaft seems to have more play than the rear drive shaft.

