That isn't what the documentation I have says. But its also irrelevant.

Hayden and B&M aren't the sources I trust.
This is a little confusing because diagrams don't scan well, but here is the best diagram I can find of the factory radiator only cooling. Note the fluid enters the radiator at the bottom and exits at the top, which I can confirm is what my jeep does, and every vertical flow cooler should do. This image is from Dorman, but is the clearest diagram I could find.
Here is from the FSM diagramming routing with the factory auxillary cooler option. Notice it runs from the auxiliary cooler to the bottom of the radiator. This jives with what the dealer mechanics claim is the correct way as well as what the transmission shop shop suggests. Don't even try to tell me they decided to route through the transmission backwards, nobody here is that dumb.
Going to the radiator first would probably remove more heat yes, but it would do it by pumping that heat into the engine coolant. Why would I want to do that? I don't. The dealer doesn't want me to. The trans guy doesn't want me to.
I'll either go trans -> cooler -> radiator -> trans, or just trans -> cooler -> trans.
I feel like this entire conversation is a lot of reinventing the wheel. Particularly in light of the fact that I've done this about 15 times before, and killed several transmissions before learning what actually works vs what people spew out claiming they expertly know.
The real point of the post, and still somewhat undecided on my part - is do I install the cooler in front of the mechanical fan or aux electric fan.
Its going to be the aux fan, and I'll have the ECU reprogrammed to lower the fan temp down to what I want it to be.