Liquid water can and does exist in the atmosphere at temperatures well below -40 as super-cooled water drops or normal drops carried aloft by rising air,
agree, moreover the gain of height (3000 ft) seems to little compared to the 7000 climb rate. May seen this as a sign of iced wings.
I do not see the need to hit the TC itself. To enter the cloud what is generated by the TC, containing huge amount of ice and supercoold liquid water is enough to overload the anti-ice capabilities of that aircraft.