Sending the analog signal 30 meters after amplification is very feasible with some attention, however I would be very cautious about the lightning and safety situation:
1. The negative side is grounded at the inverter but the current shunts are in series with the negative side which does not strike me as ideal. Even if a shunt did not fail open, there are now more connections in series on the protective ground circuit.
2. There is a ground loop through the USB connection to the computer's chassis ground. At the very least, the USB connection should be of galvanically isolated to protect the computer from damage in the event of a fault. An Ethernet connection would be even better; see below.
I have some other commends about the general design:
1. It is not shown in your diagram, but instrumentation amplifiers have another input in the form of the reference input which serves as the reference for the output voltage. So there are *three* analog signals if the two reference inputs are combined to travel 30 meters to the Arduino. When used this way, the reference input removes noise between the amplifier output and the load. It is important to show the reference input connections to properly understand how the circuit works and what is going on.
2. Placing the current shunts on the positive side may be desirable but creates complications with using the instrumentation amplifiers as I expect you found. The alternative I would try before using instrumentation amplifiers is high side current mirrors using operational amplifiers shown in
figure 10 here. The voltage range of the output is only limited by the voltage rating of the external transistor so it can be quite high. Counterintuitively however, this requires the load to share a ground for the return currents, which means it would *not* work with galvanically isolated USB without other provisions to share a ground, but I would still prefer to do it this way if acceptable, which it should be since using instrumentation amplifiers has the same disadvantages in regard to grounding and return currents and more. It is just something to think about; if you are more comfortable with instrumentation amplifiers, then use them.
Operational amplifier current mirrors can also be used on the negative side but this may present difficulties on the measurement side because the signal will be referenced to a positive voltage and go negative. I would still do this rather than use instrumentation amplifiers.
3. The safest configuration is to move all of the measurement circuitry to the remove location and connect via Ethernet because it is inherently galvanically isolated at both ends. This also allows the easy option of using Ethernet over optical fiber or Ethernet to WiFi bridges.