Just take a medium sized hammer and tap the u-joint on the side of the "U" so as to tighten the snap ring up against the outside of the grove that it's in. It shouldn't take much and the u-joint will be looser.
I've never been able to insert the snap ring into the grove if there is a needle laying sideways in the cup. That seldom happens to me anymore. One thing that really helps with this is to give a squirt of grease into each cup before installation. Smear the grease around the needles evenly to help hold them in place.
I've found over the years that automotive u-joints last a lot longer if you avoid driving through puddles when it rains and if you grease the u-joint with water proof grease. On my 1990 Cummins with just regular grease I was replacing the rear u-joint once a year. Water proof grease and I now change the rear u-joint once every 5 years.
The last time I did a u joint drive shaft that was my experience, one of the needle tipped and couldn't put it together. Another strange /odd thing, the cheaper Autozone brand had a grease fitting on it and the Spicer brand didn't, and I didn't see all that much grease in the Spicer, told my son I'd put more in, he said it's fine, so he put it together, still stiff I think.