Refill 2005 Toyota Tundra automatic transmission fluid

I made a mistake and drained the automatic transmission fluid on a 2005 Toyota Tundra with a sealed transmission. I was working too fast and pulled the AT drain plug rather than the oil drain plug. Sigh…

I am supposed to be able to refill it using a fill port and overflow port. I found the overflow port at the bottom of the pan. It is a round bolt head with an internal hex driver. I also think I found the fill port. It is in the upper tranny housing positioned left rear. It also uses a round bolt head with an internal hex driver.

The problem at this point is I cannot break the fill port plug. The hex driver slipped once so I am on the way to stripping it. I am pretty sure it is thread-locked in place so I want to try another method of filling…

My 2005 Tundra has a factory transmission fluid cooler as shown below. I would like to try to refill through the cooler return line.

I have two questions. First, is this a non-dangerous method to refill the automatic transmission fluid given my problem with the fill port plug?

Second, I’m having trouble find a genuine Toyota diagram of the cooler in the system. Can anyone confirm the fluid return line is the bottom line?

Thanks in advance.

---

Here is the AT fluid cooler:

Here is a closeup of the lines to the AT fluid cooler: