I have tried to do it your way.
I had to turn off HOTAS synchronize option next set throttles in IDLE then jumped in A10 afterwards run auto-start and it worked.
My observations are:
- manual startup isnt working with synchronize "on" and "off" option
- if I moved throttles at any time before both engines ran it resulted in failure
It looks like last update didn't fix A10C start procedure.