Designing a current sense circuit to measure a wide range of resistances and noise considerations
The 60 ohm load to 200K ohm load range is on the order of four to five decades of change. As you seem to suspect from comments in your question this is just not a practical thing to handle in the manner that you suggested.
A much better way to deal with this in a more practical way is to divide up the range so that you would could deal with each decade of load resistance value with different values of current sense resistor for each. This is evident in lower cost digital meters that have range selection switches or the higher end ones that have auto-ranging. The idea would be to use high performance analogue switch components to switch in various sense resistors. If you put this under microprocessor control you can have the MCU change the analogue switch till you find the selection that offers the highest voltage output from the amplifier circuitry. Once the range is found you can make your A/D reading.
It may be possible that all you need is the analogue switches and the various sense resistors. On the other hand you may find it desirable to have each range have it's own gain stage with each stage feeding into the input channel selection multiplexer in front of the A/D converter.