once the water reaches boiling point relative to whatever antifreeze, or pressure, it has/is under, it flashes into steam, steam expands at a rate of about 1400 to 1, it may only be one little hot spot, but if it has a chance to flash into steam it will push all the water out. That's why you need to keep it moving.

If it is happening that quickly, you aren't moving water, even with no fan, the radiator alone should give you 15 minutes or so of cooling at idle. And definitely you should see movement with the thermostat out.

The universal street rod radiator should be more than adequate for a stock 235. Did you take all the shipping plugs out of the openings?

is it bubbling like there could be combustion gases getting into the water? Do you have water in your oil? Have you looked behind the water pump/thermostat housing? Are you certain there is even an impeller on the water pump? You don't need to buy a water pump until you ascertain this one is bad, but you need to look in all the holes you can find until you find out what is going on. Since you have the fenders and stuff off, it would be easy to replace the freeze plugs, but I would start with stuff you can just unbolt.

Do you have it plumbed in like CASO said above?

When you get an old used (up) engine like this, anything could be wrong.