It works!
The baby load V1 works. Minimal circuit, just the opamp, sense resistor, mosfet and a voltage divider pot to set the input. The key was using the TLE2142 which has rail to rail inputs and close to rail to rail outputs.
Mosfet on a PC chipset heatsink (about 1.5"x1.5"x1.5") attached with one the those little plastic spring clips. The only high side stuff that went through the bread board was the sense resistor and the ground return.
I fired it up at 1A, 12V and it got too hot to touch the mosfet after about 30 seconds, a few minutes longer and the heatsink was too hot to hold onto for long. The sense resistor was cool enough to hold onto. The breadboard jumper wires groaned and smelt funny, but I could still hold them and they weren't melting.
I put a cooking probe on the heatsink and it got up to about 67*C. I used an IR temperature probe to see what the mosfet case was and the maximum reading I could get was 80*C.
However it burped and cut out a few times then stabilised again, I'm not sure if I tripped the mosfet thermal protection or breadboard shenanigans but I decided it was probably running too hard without a fan and backed it down to 0.5A and noted that the heatsink temp fell slowly to about 57*C and stayed there for another 5 minutes.
So I recon it can handle 0.5A with 1A short bursts. With a fan on the heatsink it might do 1A sustained.
This version won't give me an ability to cycle a LiPo in a sensible time, my Accucel6 can sustain 0.5A. I want something a bit more beefy. However this one might still be useful from time to time for loading electronics circuits up.
For the LiPo capacity tester I will need to build the full Peter Oakes 5A version with a CPU heatsink and fan with thermal grease and a proper bolt on the heatsink. Then I'll see how many amps it can sustain.
Thanks to everyone who helped and put up with my frustrations and stupid questions. Couldn't have done it without you.