Warren in Lancaster, PA
This is a good example of a situation where an experienced hand tool woodworker can do much better than a machine woodworker.

First of all, if you try to make your new board parallel to the three corners that are flat on the bench, then yes, you might finish out at 1/2 or worse. We don't do that. If you rock the board back a little so that two opposite corners are equally off the bench, say 1/4, the picture brightens appreciably. And if you have not yet done anything to the board, it may be closer to 1 1/8. If it is a case side, you may be able to cheat somewhere, like a back corner where there is a rabbet on the inside.

If you watch the U tube experts, they first plane cross grain everywhere on the board, even planing places that are already low. Then they plane diagonally, every where, not just the diagonal that needs it, but also the diagonal that is already low. Judicious planing takes nothing from the low spots.

My hunch is that your board could be made to answer at 7/8, but that it would be hard for an inexperienced person could do it.