Thinking
6x13x2 stacked plate

My config:
1964 Chevy 2, LS3 (cleaned up, cammed, & small nitrous hit), 4L80E (Typical +1000HP build), 3400 Stall, QP Fabbed 9" 3.70 and 26" tires. Street Strip deal with a 8.50 cert. I know I'm not going there with this motor but the car has been there before and your always a ring land away from "while I'm in here I might as well".

More details

The car see's mostly street driving now which is done mostly on country roads but I get into traffic here and there but nothing usually that long, for context I wait in staging lanes longer than any traffic this car will see.

Right now I'm looking at a Derail Stacked Plate unit that is 6x13x2. That is as big as I can get behind 1/2 of the grill of the '64, the latch/support prevents using the entire area behind the grill. Roughly half of that space would be exposed to the Radiator opening in the core support, the other half would have an air gap but sit in front of the steel portion of the core support which does have 2 large relief holes to support air flow but I figure it has to be a bit restrictive so I thought I'd mention it. Oh and the radiator opening has an entrophy rad and a AC condensor so pretty full on this half too.

Here is the link to the part I'm considering.
https://www.summitracing.com/parts/der-13402?rrec=true

My other option is to keep the cooler mounted under the car and put a fan on it, simple enough to do as I already mounted a unit under the car, just not sure it's big enough (5x10x1 plate not stacked) as I never see the temp level off during a 30 min drive. Temps climb slowly to ~180 and its looks like it's gonna keep going but I haven't found out since I'm still not driving it longer than 15-30 minutes.

I guess I also didn't want to wire in another output.... this poor car wasn't built for this much wiring and heat.

 

So you currently have no auxiliary cooler at all, only the one in the radiator?

 

Not nearly hp wise as your hot rod but I have used the B&M stacked plate cooler on a few LS/4L60E swaps with great success. They measure about 11" x 11" cooling area.
Pic of my latest 80 project trans cooler set up. At slow speeds and higher heat times the electric radiator fan will pull air thru the trans cooler. The ECM controls the radiator on and off of the fan.

 

I have a small cooler mounted under the car now that I don’t think is cutting it. I do not plan on using the cooler in the radiator.

 

I wish I had that space! 11” by 11” is a luxury I don’t have in this car.

I have done similar setups to yours in the past and agree, that size cooler and location is great!

 

This gives you an idea of the situation, I could go with hood pins and pull the latch out (probably long over due) but this car has all of it's trim including the non-func gas cap and antenna which I think is a cool look, especially at the track so I didn't want to add hood pins. Honestly whats going on under the car relative to the size of the cooler I can run isn't awsome either but at least it wouldn't add more heat under the hood so that might be another reason to add that fan and keep the location under the car. Problem there is it's gonna hang low, probably not the lowest point on the car but one of them. Especially if I go with a stacked plate, those are ~2" thick, then add a ~4" fan.

https://photos.app.goo.gl/QFkULrbB27n7FR6V7

So anyway back to my orig Q, The area of a similar brand stacked plate for an 11x11 is 121, the 13x6 is 78, I'm gonna guess without a fan 13x6 ain't gonna cut it but I'm going to chat with a vendor shortly and will post some info up as I suspect regaurdless of other variables (like air flow, air temp, driving prefs, ..) there is a minimum amount of surface area required to dispurse typical heat generated by a <name your tranny> that I should be starting with but I can't find published info?

 

That cooler is plenty. I have a similar one but slightly smaller and my temps are in check
EDIT: sorry I didnt catch the pic of the car above wasnt the OP

But, my statement still holds true

 

Run your existing one in series with the new one.
whichever one you suspect is less efficient should be ‘first in line’ so it sees a higher delta t

 

Following up:

I've been running around more with a Spal 325cfm fan on the current 5x10x1 plate cooler. It's not enough, if I just drive around normal it gets to 180 pretty quick and thats with fan on at 170, climbs a little slower to 190 after that but I'm calling it no bueno.

Going to step up to a 7x13x2 under the car and stick with 1 fan for now and see how it does. It will be tight (whats new) and it will hang a little lower than I want (whats new) but I think that will do it, its alot more area and the fan moves a good amount of air.

I can get another fan on there if needed AND/OR as mentioned above I could try to squeeze the current undersized cooler in front of this new setup but one step at a time...