The failure documented here is pretty typical of a chip / board destroyed by having been powered by reverse voltage. The reason the chip appears to be okay is because when powered off board, the trim input is not being tested.
The AD587 was first trimmed to very near 10V by two resistors about the trimmer, to Vout regulated, and common respectively. After hours or semiautomated testing, the series resistor for the Vishay compensating thermistor was determined. The small correction current developed by this very fine correction was applied to the trim pin. Hours of final testing and calibration followed.
So, I think what has happened is that internal trim circuit is damaged (destroyed). The reason there may be some correlation to the jumper is that the jumper connects the trim.
Because the fine temperature trim was unique to each individual AD587, once an AD587 of a SVR-T board was destroyed, there was no repair. So, it was okay to use the thermal epoxy to get good thermal coupling between the thermistor and thermistor series resistor to the board itself.
Another reason the chip might be showing some signs of life is that for SVR-T boards, the AD587 was preselected, generally for an uncorrected tempco of better than about 3 ppm/c. After correction, the SVR-T board tempco was typically better than 0.3 ppm/c. Without the internal damaged trim circuit, there apparently remains a pretty good "raw" output, which however, can no longer be trimmed because the trim circuit is damaged.
We never spent much time looking at reverse powered boards, because all of the passive off chip components were likely okay. These boards just went in the trash.
I took the AD587 off of the board, placed it into a machine socket, and clipped 15V and the meter leads to it, and I am shocked at how stable and low noise the output is. And this is without any capacitors or other circuitry at all! Just the IC in a socket!
Here's ~20 minutes of data (attached).
EDIT: adding photo of connections