The stock Eaton differential in those trucks is a relatively sturdy unit. Some movement is normal.
You didn't say if it was noisy. Check the universal joints and the rear flange. Pull the rear cover and take
a look at the gears. If there is no obvious damage or wear, change the oil and move on.
It's a lot of work and expense to change out something that could be serviceable.
Fred


1956 3100 Pickup/Red/350/3sp OD/PS/Disc Brakes
1957 Bel Air Sport Coupe/Red/355/TH350/PS/Disc Brakes
2017 Silverado LT Single Cab SB/Black/5.3/6 Speed Trans
1947 Willys CJ2A w/F-Head engine