That kind of wood is expensive where I live. I would make the drive or (probably faster) build a planer sled. It will get you through this build and any others down the road. This one got me by without a jointer for a long time.
It is low profile but the torsion box construction has kept this flat for years:
These cleats and wedges are the adjustment mechanism:
The bungee keeps the cleats on board (no pun intended):
It will adjust for some severely whacked boards:
Any sufficiently advanced technology is indistinguishable from magic.
- Arthur C. Clarke