After rereading the post it may be possible. Your description was actually wide open compared to most and I took the words 'immediately shifts into like 3rd-4th gear' for what they are instead of grasping you likely forced a downshift by getting into throttle deeper trying to get the car to go faster.
I am likely wrong, your guy may be dead on. I have transmission on the brain lately, a lot of posts on them.
Your mileage is as well too low to already have trans wear of the type I proposed.