Rodding and cleaning an almost 90 year-old Model A radiator may sound well and good, but how are you going to reattach the inevitably separated fins from the tubes? This is an overlooked area in cooling that is critical to dissipating heat from the coolant through the radiator. Those fins aren't there for looks! Once the fins have separated from the tubes, I doubt that they can ever be efficiently reattached.
In the OP's case, it would be more prudent to simply belly up to the bar and purchase a quality THREE row radiator from a reputable vendor, such as Brassworks or Bergs's, who supply the large vendors. Stay away from the cheaper, thinner two-row radiators, whose lower price seems attractive, but won't cool worth a tinker's dam anywhere except in northern Minnesota during an arctic ice storm in January. This is one area where ya' gotta' pay the full admission price in order to enjoy the show. With the possible exception of a cheap battery, there are very few areas in a Model A that will cause more misery than a poorly functioning radiator. 'Been there, 'done that. Don't waste money on quick fix cleaning and "flow testing". Our radiators are usually too old and worn out to ever approach the original cooling design efficiency. Install a quality radiator and that'll be one less constant irritant in your Model A enjoyment.
Marshall