Yeah...exactly my recommendation, except you're describing the fluid flow backwards.In warmer climates like here in Texas, I do the GM method myself. From the trans into the upper radiator port, then from the lower radiator port to the inlet of the auxiliary cooler then back to the trans. This is how both my Express van and Tahoe were factory plumbed.
The hot fluid coming from the trans goes to the inlet of the aux cooler, from the outlet of the aux cooler to the lower rad cooler port, then from the upper rad cooler port back to the inlet port on the trans, where the cooled fluid lubes the geartrain.
Remember that the inlet to the rad cooler is the lower port, and the outlet is the upper port.