I see more problems. Lots of them.
The through core zip ties on the large cooler are not nice to the core.
The small cooler is mounted so far in front of the radiator and has no ducting, it won't provide any low speed cooling. What air the fan draws in will just flow around that cooler.
Mud and rocks, lots of convertor load, zero vehicle speed. You are relying on airflow for all transmission cooling.
Why the aversion to the in radiator cooler? To this day that is how nearly everything does it. The latest is an out of radiator oil to water heat exchanger. But it is still an oil to water heat exchanger, just more plumbing on the coolant side. I think a lot of these are being plumbed to put heat into modern transmissions that run a lot of convertor lockup to be more efficient. But a C4 doesn't lockup and just builds heat as the transmission slips.
I would run the in radiator transmission cooler and ditch the small cooler hanging out not being effective. Remount the big cooler to not be stabbing through the core.
If you still have an extreme aversion to the in radiator cooler you have, run an external oil to water cooler. Back in my overkill days I would probably come up with something like a remote engine oil filter adapter plumbed into the transmission cooler line, get a spin on transmission filter out of it as well. On that oil filter mount add an engine oil cooler sanwich adaptor (like the factory Explorer oil cooler, mustang SVO oil cooler, etc.). But where to feed it water? Tap the back of the intake manifold water crossover. This will be a source of water that has passed through the block but before the head. Warm, but not hot water. Then where to return it, Tee into the heater hose return into the water pump. Not going to be as good as the in radiator cooler, but will still give a heat dump into the coolant. Which is ideal at low/no speed high load use. Gallons of water has enough thermal mass to absorb thermal spikes.