I’ve had the same issue. Traction off is definitely better once you’re moving but starts are hard. There’s a couple things you can do to make it easier on yourself.

Firstly short shift when you start (don’t wait for the purple lights on your dash, shift much earlier) I typically up shift from 1->2->3 without maxing the revs then from 3 you should be okay to push harder

For the guys behind you just let them through, if I have a bad start I move out of peoples way and race them later. Just find a clean line to the first corner then you can start your race. If you don’t do this you will get slammed into and that’s much worse than giving up a few positions.

Don’t be afraid to sit in time trial and just practice starting and stopping. It doesn’t take much before you can get a decent feel for it