I bought a new Lock-right for my front 60 several years ago and have never had any problems with it.
The springs should fit in the slots really tight and there is no way they could "pop out". Mine were a PITA to get compressed enough and slid into the slot. Also, the springs are used to unlock the diff , not to lock both sides together. Same thing with the small pins, they are simply there to give the two pieces something to slide on.
I'm not sure on your post, but have you actually put everything together and tested the truck with it installed...as in driving around in 4wd. Or are you testing it by spinning the tires by hand with them off the ground?