To go along with my oak flooring I am redoing the stairs that was carpeted.
I have a 44" x 44" 1" thick landing made up pf glued 4" oak boards.

I was going to just nail it down but now I am concerned over it splitting with expansion and contraction.

Will construction adhesive allow it to move if I just put a couple of nails in the middle?

Go over it in the opposite direction, or at a 45º and you will be fine.