With due respect...

I would first flush the coolant system. Drain at right-hand rear bottom end of block, or at oil filter coolant line if you have water-cooled oil filter base. This to get any crud out of engine, which will otherwise start plugging your new radiator.

Second, I would do the tranny flush, but not reconnect return line, but instead then do the radiator replacement.

Suggested trick by using two wrenches, pushing them together has worked fine for me.

Also follow suggestion to replace the short rubber coolant lines to oil filter base cooler (if you have one, see above). I almost lost my engine from overheat due to failure of one of those. They take a lot of heat from hot surroundings and become quite brittle despite they look good from outside.

Gustafkalle