Spinning caps are a good indication that the yokes are worn and failure is eminent. When installing a new u-joint, take note. If the cap slids in easily, the yoke is worn. A good yoke will be slightly under size and offer an interference fit (you will have to use a hammer to tap in it.) The reason the caps spinning is due to the fact the holes for the yoke is oval and this happens from stress or shock loading. For a emergency trail repair, welding isn't a bad idea but as a long term fix it's not a good idea because the heat from the welding will further weaken the area.
The correct fix would be to replace the axle shaft and the stub shaft. Generally for myself, if I have a failed stub shaft, I replace the inner shaft as a just in case factor this way I know both units are fresh.
When installing new u-joints I recommend installing them dry without grease and painting a witness line across the yoke and cap so you can easily spot a cap rotating. We have done the c-clip conversions in the past but I personally don't think the c-clip mod is any stronger then the stock set up. The CTM or OX u-jonts are much stronger but both makers do not recommend using them without a hub conversion. The CTM and OX u-joints and not designed for freeway use because they would wear faster due to the bushing for the caps rather the roller bearings. Also the CTM and OX u-joint in a stock axel shaft will require grinding as well so the shoulders will clear. I would recommend using the Spicer X series u-joints, they are stronger and came stock with the Rubicons. Also with the X series u-joints be sure to keep the same caps on the same legs you pulled off. One of the great things are the X seris u-joints is the grease is premeasured and it is exact. There is no reason for you to add grease and there is a triple seal that will keep out water and keep grease in.
My .02 cents on the axle shafts for the Rubicon is the stock shafts are on the delicate side. The stock 4:1 will pound them. If you are running trails that do not require the front locked, keep them unlocked, this will reduce the stress on the front axle and let them live a little longer. When fully locked on more technical trails, go easy on the skinny pedal and be smooth. Everything from the motor to the tires will love you more and live a lot longer. If you have to up-grade, go chromoly but only go stronger u-joints if you run a hub conversion.