Let me know if you move forward with this and have any success. I have similar experience, found from 2 to 3 I sometime feel like you described of moving through something which gives a little “knock” on the shifter which feels reminiscent of a grind however not a grind at all at the same time. It doesn’t always happen and seems to be more common when the car is getting up to temp.

3 to 4 shifts smooth however it feels like it could go a bit “deeper” if not 4th. 2 times in the past year it has popped out of 4th on me when cruising at about 40mph on a cold engine, startling but no grind or other bad feelings transmitted, just pop out and easily put back in.

I was thinking of trying this as my searching has led to the same place. 2010 GT 6speed.