I have powered up my variant of Jay_Diddy_B's ESR meter, and it is performing very nicely indeed.
The IA certainly allows easy setup up for 0 milliohm (+/- less than 0.1 milliohm) and 1.000V for 1 ohm 1%, and appears to be dead accurate down to the 47 milliohm 1% reference I have, when using a nice 30cm long Kelvin clip lead set with 4mm plugs.
I haven't yet played with the 555 oscillator, which is running at 18kHz, to see if the setup can support similar results at 100kHz.
Aiming to set up the IA gain for 1V/ohm and 0.1V/ohm to allow up to about 16 ohm max range (open circuit reads about 1.65V at the moment), and use switched fixed resistors and a trimpot for gain setup with sufficient offset trim range (which I aim to change to fixed and trimpot to reduce the present trimpot sensitivity when setting 0 ohm end).
I found a practical 'zero ohm' link to keep the Kelvin clip contact faces flat over their entire length, in the form of an 8mm wide, 0.9mm thick flat bar that had a previous life as a contact link bar in a high current contactor. There are a few parts that show some temperature sensitivity (a few milliohm change when squirted), so packaging the circuitry to minimise local temperature changes seems worthwhile.
PS. it does work with capacitors, even the bigger ones with readings down around 10 milliohm, although ESR of a cap may be quite temp sensitive and so absolute ESR should really note the temp, and comparisons should use caps at the same ambient temp.