Just started my 15 min upload, took the time

Here is a way

            *- 100k --*
            |         |
--*-- 100k -*-|      |
  |           |      |
  2           |      |
  5           |      |
  0           |   /---*-- out to adc
  R           |  /
  |           | /
--*-- 100k -*-|/
            |
            |
            *--  100k --> bias pot, adj for 0 V out @ 4mA
            |
            1
            0
            0
            k
            |
           Gnd

The resistor values are 'grab bag' but the circuit works and the input is not referenced to ground.
This is a unity gain circuit, cange two resistors to change the gain.

The 2 unlabelled wires to the left are the 4-20 connection.

Erik

PS
for an industrial unit I would reduce the 250 Ohms to 100 and make the op-amp have a different gain.