I cranked it all the way up to 100% duty at 24v, and it got to 146 amps. It's still with just 2 mosfets and 2 diodes. The bus bar stayed cool. I'm sure it will warm up with all 12, but I feel much more confident now that it won't be trouble to get the heat removed. The base plate was the same temperature as the bus bars, so the thermal transfer was very good.
Notice that the spike is clamped at around 18.5v or so. The TVS diode temperature was climbing at about 1 deg C every 5 seconds. It would probably find an equilibrium temperature at some point, but this represents about 876amp if it was all 12 mosfets. So, I wouldn't be putting much more current through them. 167amp represents max current the pair would ever see.