The underside supports (aprons and batons) are there to help keep the top flat. I added them with screws and liquid hide glue.
Unfortunately the batons couldn’t go straight across the full width because of table slides that need to pull out at each end.
I made table slides for the leaves using Accuride Heavy Duty drawer slides and attaching thick oak to each side (aprons and runners).
The leaves also got the underside support treatment. You can see in the foreground the elongated holes to allow for wood movement.