I think everyone else covered the why and all that...I just had another thought I wanted to share.

Since you know you're going to freak out if you go over time, could you maybe ask your T to help you do some kind of mindfulness or grounding exercise right at the end of session? Even if it means going over just a bit? That way, you could experience going over time in a calm, controlled manner, and maybe it would help to ease the panic and build a positive experience of going over time.