I also have a (newer) 5442A and investigated on the interesting stacked 13V reference.
This stacking circuit is partly on the small reference board with both SZA263, and partly outside the oven assembly, if I remember correctly.
Maybe you print the different parts of the schematics to understand how this circuit works.
I don't know, where exactly you probe these 13V. W/o extender card it's also not that easy.
I suggest that you connect two cables directly on the reference board choosing ground and a connection directly at the upper SZA263 output, and then analyze the signal in situ. Pay attention not to create any shorts, especially by proper selection of isolated cables!
I doubt that the SZA263 itself is damaged. Maybe one of the LM308 is breaking down thermally, i.e. one of its input transistors, as the whole assembly is at about 55°C permanently.
Maybe you might also dis - connect the reference board and rebuild the stacking circuit on a test board at room temperature, so you can decide where the failing OpAmp, or other component is sitting.
Another idea: As the oven might also have problems, check the stability of the supply voltages.
Frank