You only mentioned changing one U-joint, check/change the other one. U-joints are like rear tires, usually change both at same time. (Don't rotate them to the front!
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If you are running on old tires, sometimes the cords in tires will break allowing it to go out of round at higher speeds causing vibrations. This usually happens towards the end of tire life, but the cords do not need to be exposed for this to happen, and is very hard to diagnose.