will finishing off body welds make a difference ?

Back in the day when these cars were new, the racers like Sox&Martin and Dick Landy would reweld all of the factory welds and body seams to strengthen the cars a lot. This was standard practice.
So, does it make it make a difference?
Hell yeah!
The factory welds are mediocre at best, and most people can see this as easily as you have.
However, if you have a valuable rare car, you would decrease the value by rewelding or modifying the factory as built chassis, even if it was a lot better to do so.
BTW, i am a journeyman welder that has a lot of experience looking at factory and modified cars over the years, paying a lot of attention to how they were built and the quality or lack thereof from the factory vs modified.
Food for thought...........