The problem you described wasn't the OLED, so replacing it wouldn't have changed anything.
The cable should be fine I was able to make it an inch shorter only, so that's not the problem.
I don't know if you have the service manual of your Wavetek 4950 and you happened to study how the image on the two displays is built starting from the serial data stream.
However, on the display located on the right, the raster is built by sending the first and twenty-first character, then the second and twenty-second, then the third and twenty-third and so on. So if for some reason there is a timing problem the 1st and 21st characters can be misread and show uncertainty (As it happens now).
Adding an unexpected device (the new display circuit) may affect the stability of the existing system.
I initially had this problem myself and fixed it with a software delay.
Unfortunately now I can no longer access the computer and the compiler that I used at the time to create the code and I can no longer make changes.
The only thing you can do is introduce/modify a hardware delay on the data line of the signal (a capacitor, C6 1nF*, already exists on the Data-IN line). Try decreasing or increasing it.
* on the original Datron/Wavetek Display Board.