I have done a bunch of them, it is way easy. It is a little hard to explain.
I had an old time welder guy show me this trick 30 years ago, and it has worked well for me. You could grind off the old weld and clean that shouldered end up enough to get it to fit back on your square re-cut drive shaft.
Or cut the section out of the middle that you don't need, and split that waste section lengthways, hopefully you are cutting out at least 6-8 inches, longer is better. I use a plasma to split the waste piece, and I usually cut it on it's seam. You may need to cut out 1/8 to 3/16ths. Now the tricky part. Squeeze the waste piece down until it fits inside the old drive shaft. Tight. Put half of it in one end, and half in the other. Match the seam in the good piece to the split in the waste piece. Time the shaft, and weld it up. I usually seperate the two ends about 3/16ths and weld deep, to all three pieces. If this does not make sense, ask me questions. I started doing these for off road applications, but they snuck into street trucks with no ill effects thus far.
Disclamer: The previous statement was made by a professional driver on a closed course, your mileage may vary, not available in Alaska or California. For a complete list of all rules, watch your mailbox.