Those are some pretty ugly cuts, looks like someone was drunk with a Sawzall when they did it. I'd re-cut each pipe just enough to get a clean edge and then use a 2.25" ID pipe to couple the pieces back together. Good luck.
I had my original exhaust reinstalled/welded last month. I took it to a small local exhaust shop with great reviews. The old guy owner did a great job. I know nothing about welding, but he said due to the internal corrosion and the thinner metal, he didn't use a traditional welding method. He used a torch and a metal rod. He heated up the ends and melted it all back together. Looks better than I expected too.
Could be done, just take some work to make it look decent.
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Did it with my red car when I bought it. Just had the shop use a GT exhaust bends he had to replace the over axle section from the mufflers to the OEM stainless ends. Was less than a $100.