Fixing a curved fence post

I recently sunk some 4x4 pressure treated fence posts into the ground in my yard, secured by concrete. Most of them are fine, but one of them, I guess I didn’t give it long enough to dry before doing so, because while it was nice and straight when I put it in, and it went in straight and level, it has curved significantly since I put it in. The first foot or so of it out of the ground is still going straight up, but if I draw a plumb line from the edge upward after that point, it ends about 2" (more than halfway) into the top of the post by the top.

And, of course, it’s the one I want to attach the gate to, so it has to actually be pretty level or the gate will not work well.

My plan to fix this is to cut it down that plumb line so that the edge where the gate attaches is straight up and down, then glue the offcut to the other side so it’s more-or-less still the right shape (less the saw kerf), then glue/bolt/screw a 2x4 to the side away from the gate to give it some more strength.

Is this a reasonable idea? Got a better one?

Your approach sounds perfect.