Assuming OP's Tahoe has the factory trans cooler, a larger one is unnecessary IMHO. 190-200° F is normal operating range for the 6L transmissions. Dex6 has substantially better high-temperature capabilities than Dex3. And low temps can be just as bad, or even worse, than high temps. If you're not getting above ~150°, you're not boiling off condensation that may have collected in the transmission. And we all (should) know that water in the fluid is bad.
I just have the small factory cooler in my Suburban. 240k miles, still original, still operates perfectly. And I beat the crap out if it. If I'm just driving, I'm cruising down the highway and high speeds (90-100+), or I'm towing either my 4,000-lb cargo trailer or 8600-lb travel trailer.
My personal record is 243°, usually achieved when I'm going over the Continental Divide with the travel trailer. I simply change the trans fluid more frequently. Sometimes with an interval as low as 30k miles. But usually I do it every 50k. Full flush - at the dealership. 16 quarts.
This was on I-70 eastbound towards the Eisenhower Tunnel, 7% grades, pulling the behemoth right at 16,000 lbs gross vehicle weight...
Tiny cooler:
