I don't think there is much you can do about the warp. Any attempt to moisten, heat, etc risks making it worse and strongbacks/battens could crack it. Once it's warped like this, hysteresis will prevent it from ever being flat again without cutting/planing and re-gluing. Water swells the fibers, so the wet side will become convex, which is potentially what you'd want to happen to the top. This will happen regardless of grain direction in the individual boards. But it won't be even across the top and there is no practical way to control what happens.
If you wanted just to try something, turn it upside down on the grass overnight or for a couple days. Don't let it get rained on. The moisture in the ground will migrate to the top and may reduce the warp. But a day upright in sun will put it right back where it is.
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