That's what I did (well, not exactly that, but I asked for the guys mending my exhaust to do the "strongest" job they could). And I also told them I wasn't worried with how it looked, function before form.
But in all honesty I don't think making the exhaust structure stronger at the breaking point will solve this. This particular breaking point is different from the first.
Here the pics:
1st exhaust:

2nd exhaust:

So ... if that particular weld gets stronger, the vibration and resonance will just find a third weak spot.
I do believe the mounts are incorrectly placed, and also that there must be a flexible section before the silencer. But I'm not an engineer and it's not up to me to do Morgan's job.