Haha. Yes, that's seems to be the culprit for discomfort ! Two other issues that I should pay attention to is guiding the movement more with my hips and slowing down on the eccentric part of the movement.

Yeah, those are running shoes but with minimal cushion and a flat sole. I've used those for sometime now. I know that a hard sole is ideal but I've had no issues with it till now.
I used to Squat with one that has thick cushion to 'absorb the impact from running' with a rounded sole (by Sketchers). Boy am I going to remember that mistake. It's great for running but I find it terrible for casual use. I almost tripped on multiple occasions whilst walking because I 'kicked' the floor.