If your need is only for occasional measurements, it would be easy enough to create a battery-powered wireless milliammeter. For example a shunt resistor, op amp and a microcontroller with some kind of wireless communication (eg. WiFi or Bluetooth).
Another approach would be to make a current sink circuit using a high voltage MOSFET that operates at the -1100V rail. The Hamamatsu C9619 is capable of 2mA current so you have a fair bit to play with. You would have to use (continuous) high voltage rated resistors for the power dropper (and, to be prudent, in series with the high-voltage N-channel transistor drain). A very low power op-amp and a very low Iq shunt regulator for the power would complete the circuit. Recieving it would be a transimpedance amplifier referenced to ground. Pick the series drain resistor to limit the current to a few mA.
simulate this circuit – Schematic created using CircuitLab