Looking through the user manuals, it seems like the OVP circuit cannot be disabled and is on all the time!
Some links seemed to suggest that the problem might be a sense error (open or shorted sense lines are an Achilles heel for this model of supply), or perhaps a poor choice of wire size (it's not clear how this could be a problem, it sounds like a bit of a desperation suggestion).
We eventually learned that, counterintuitively, the cause of our troubles was that we had been setting the current limit too low. The box we were powering draws much more current than we had expected, and by setting the current limit to a less conservative level the OVP shutoff does not get tripped. Why this wasn't an OCP error instead is a mystery.
Here are some links:
Here is the user's guide for the N6700. Very little ink is devoted to the OVP in this manual. http://literature.cdn.keysight.com/litweb/pdf/5969-2937.pdf
I found an older version of the manual here, which has a tiny bit more about the OVP, although nothing about what our problem turned out to be. There is mention of a SCPI command to disable OVP "tracking," this is not apparently the same thing as disabling OVP as other sections of the manual clearly say that OVP cannot be disabled. https://www.topdogtest.com/inventorypdf/N6700usr.pdf
Here is a very interesting forum thread where somebody was having trouble commanding an N6700 setup of OVP, and the problem was actually an error in the Labview driver VI because the structure for commanding the OVP does not include a setting for enable/disable. Because it can't be disabled, I guess.
Here is the article from Keysight with several guesses as to what can cause an OVP error. https://keysight.jiveon.com/community/keysight-blogs/general-electronics-measurement/blog/2017/03/09/what-can-cause-a-power-supply-output-voltage-to-exceed-its-setting