From years of observing and listening to ATC, I’ve noticed that in real life controllers initiate handoffs before the aircraft reaches the sector boundary. In BATC, this doesn’t occur until after the aircraft has crossed into the next sector. I imagine the actual ATC consultants you have could verify this.
I do understand if this is a technical impossibility because BATC isn’t notified by MSFS that the aircraft is crossing into a new sector until after it’s happened. But if it’s at all possible, it would be good to have.