I wouldnt call myself an expert but I know BBCs quite well.
Every suggestion so far is pretty good.
If I understand you correctly, when you come up to temp you start getting extreme needle swings on the mech temp gauge. Fluid does not change temp that quick. You almost have to have air entering the system somewhere. Assume you have Murphy switch.
At temp, if you have a compression leak (gasket) going to the coolant you should see bubbles in the radiator.
Is your temp gauge in the intake or mid head mounted? in the head is a more consistent reading.
A cavitating water pump impeller can create havoc on your coolant, especially at high rpm. But it can still do it in a low rpm application like your irrigation pump. I would go there first, especially when you say it runs fine with a hollowed out stat.
Have you been running this for a while and this just started happening?
I spent most of my time drag racing BBCs, but they havent changed in a long time. Only difference with drag racing the boom is usually louder and more catastrophic when the engine lets loose.