The combination of low resistances and low max current makes it difficult for using a 12bit ADC straight up, like many built-in ADCs.
One option would be to use an uC with 12bit built-in ADC and external V_REF, like one of the STM32s in the right package, in combination with a 1.2V voltage regulator. That would give you an LSB of about 0.3mV. The regulator could be made using a voltage reference, opamp and a pass transistor.
Then you could put the e-fuse in a simple resistor divider circuit with say a series resistance of 150 Ohm, a 150 Ohm resistor in parallel with the e-fuse. That would give you relatively easy <1 Ohm discrimination, yet still easily discernible readings in the 1-100+ Ohm range. Max current through e-fuse would be ~8mA.
One advantage of this setup as I see it is that if you have a beefy enough regulator (10mA per channel) you don't need to mess with analog multiplexers by just powering all the e-fuses at the same time, using the plentiful analog channels on the uC for measuring. It should also be relatively easy to use in conjunction with the high-current "fun time" driver circuit, using back to back mosfets to "isolate" the measuring circuit from the e-fuse.
Then again I'm no expert so