A T-stop should feel like you're scraping the ice gently with the outside edge of the stopping foot, shoving that snow under the tail of the gliding foot blade. You really have to bend your knees and turn the stopping knee out to the side.
Dragging either edge makes you turn if you put weight on the stopping foot, so keep your weight forward over the gliding foot/bent knee. (One shoulder on each side of that foot, nose over toes.) Turning also happens if you allow your shoulders to twist to one side, which sort of goes with weight balance.
Try skating along a hockey line with the free foot posed above the line, perpendicular to the gliding foot. Always position the foot in the air so the (soon-to-be) stoping blade is angled towards the outside edge - the outside ankle turns downward.
Your head and upper body should face the wall where the hockey line stripe goes up to meet the glass. I tell skaters to make a "T" with their shoulders and spine so they don't twist.