The only other possibility would be that someone within the Sea of Eden at ground zero in 12000 BC would be sent to 2400 AD upon attempting to leave it, and someone in 2400 AD upon entering the Sea of Eden would be sent to 12000 BC inside the Sea of Eden upon attempting to enter it.
This might seem very counter-intuitive and confusing at first, but think about it - it actually works.
Between the interval of 12,000 BC - 2400 AD, anyone that enters the Sea of Eden from the past is sent to inside the Sea of Eden in the future.
Likewise, between the interval of 12,000 BC - after 2400 AD, anyone that is inside of the "real" Sea of Eden in the past will be sent to outside of it in the future, and anyone outside of it in the future will be sent to inside of it in the past.
In this way, no one needs to be shunted and we do not need to abuse the DBT card too much, although it does make for a rather strange temporal structure for the boundary of the Sea of Eden, and I don't know if it would stand up to scrutiny to be honest.