We are trying to measure a 2V signal across a current resistor at -17kV from ground.
There is no way we can put the resistor on the ground side.
We can measure this signal with a multimeter, taking care to keep it isolated. But can anyone thing of a trick to log data from it for a long period of time? The must be some trick, perhaps with a current mirror and an opto-isolator, to get the voltage down to low voltage levels.
It depends on what measurement rate/bandwidth you need. The low voltage floating at high potential is going to be a challenge for any non-galvanically-isolated differential amplifier or mirror circuit.
There are some multimeters that have long-term data-logging capability that you may be able to float if this can be done safely. If you need high bandwidth (and are not budget limited), a couple of the big scope manufacturers are now offering fiber-optic fully-isolated probes that are designed to be floated at both high potentials and at high frequencies. There are a few analog-signal-over-fiber-optic links out there that do something similar at lower cost (but still somewhat expensive).
You could use a USB-over-fiber data link and float the entire PicoScope and a battery (or use some other HV-isolated power supply), but this would have the potential hazard of the entire scope and associated cabling floating at high potentials. Fiber-optic cable often does not have any metallic content and should provide reasonable high-voltage isolation. Outside of electrical hazard, the other possible issue is that having a physically-large object connected to a high-voltage circuit may impact circuit operation if high impedances and/or low currents are involved (especially if the scope is floating at a non-DC voltage).
If you were considering building a circuit to measure the voltage and send the measurement to a ground-referenced scope or data logger, I would recommend a circuit that modulates the signal into a digital signal (such as a delta-sigma modulator), transmits the digital signal optically, and then demodulates the signal to send to the scope or logger. This may offer better long-term precision than transmitting the analog signal.