First thing, you'll mess up the springs if you push the cross shaft in straight. The directions say to twist it as you push.
Did you do the check block test? Step 31. If it doesn't fit, it's not put together correctly.
Did you do the tire spin test as instructed in steps 40-44? You need a helper for this. Turn one tire forward and hold it tight. Then the other person shouyld be able to break the other tire loose going in the opposite direction. Perform this step on both tires, going forward and backward.
Weird, I thought the directions were very clear and well-written. I have No-Slips front and rear. And I had never opened a diff up in my life.