With luck the new pedals will solve your issue, but I'd advise in any case that you examine the crank carefully for cracks. The cranks are presumably close to fifty years old and it would not surprise me to see that metal fatigue is occurring. If there are any cracks, they may be difficult to see at first but if you use magnification and bright light they should be apparent. Installing the pedal from the rear of the crank and stressing it during your exam may help.

Good luck.