I would be willing to bet if you just simply put a trans cooler on with no fan, and mounted it up front like your current cooler is mounted, when you run the radiator fan, it will also help keep the trans temp down. If you are going to go with a fan + trans cooler, then a Jones pump would be more beneficial so when the car is off you can run the fan and jones pump at the same time, which will cycle the trans fluid instead of just cooling the trans fluid that is in the cooler.
I have a simple trans cooler like in the summit link, but no fan. Hottest my trans ever got was 210, and that was after 9 rounds, and round robin racing from the 5th round on.
I also agree if you have a problem with trans temp in round robin rounds, a synthetic fluid would benefit you, or a semi synthetic.