Another potential problematic aspect to welding heavy gage metal with a torch is warping/twisting of a long 5-sided box. Further heat/cooling stresses can be imposed upon the relatively fragile core when the tanks are installed with said torch.
The magic/miracle aluminum repair rods would likely minimize the potential problems associated with the higher O/A welding tip temps and the much wider HAZ.
As mentioned previously, aftermarket trans oil coolers are widely available, and fairly easy to install.
Fixing bad designs is generally a lot of effort.. sometimes effective and worthwhile, sometimes not. Mating plastic tanks to metal radiator cores was never a good idea, and replacing the SAE/genius OEM idea with a better quality heat exchanger is the best solution, IMO. Military, aircraft or industrial surplus solutions can be found, but may turn into a quest if one doesn't know what to look for.
Finding a new, quality, SAE all-metal radiator would be a cost effective solution, even if it's not a direct replacement/identical part.. the mounting holes can be adapted to fit (sheetmetal extensions added to the mounting frame) without modifying or risk of damage to the radiator itself. Fabricating mounting brackets for a fan shroud wouldn't be extremely difficult (another OEM fuckup, supporting other parts with the radiator core). BTDT.. had a decent radiator from a Buick Special, and installed it in a Mustang many years ago.. air flow, check.. water flow, check.. TLAR, done.
I've encountered 2 faulty plastic tank versions, Ford and Chrysler, and both were just bad designs.. I didn't see any practical point in spending time on trying to improve a used (otherwise good, but used therefore questionable, core), even though my soldering skills are fairly good. An experienced radiator rebuilder would probably see those situations differently, particularly if the repair was for his own vehicle.