Assuming the welds hold, the only strength increase will be the spider gears. The R&P and stub axles will not be helped, and quite likely be subjected to more stress depending on how you're driving.
315's all by themselves aren't going to fix your problem. In fact there isn't any one thing that will. If you want to try something cheap, remove the rear bar and droop limit the front. Again, it won't fix it, but you'll see an improvement. You can also play with droop limiting the rear, shock adjustments, alignments, etc, etc. I would be thinking about these types of things long before a welded diff.