Impractical? I think the wet grass + sun idea sounds fantastic!
I see two options here-
Wood is shaped with the application of moisture and heat. Run it through some steam in the dishwasher and while it is still piping hot clamp it tightly between rigid boards to dry. This method works with all kind of wood shaping but you should know that there is always the risk that the stress will cause the board to crack while it dries.
For descriptions of this technique google "wood steam bending". Most results will describe using a specialized steaming chamber rather than a dishwasher but the technique is the same.
The other method is mechanical: use a belt sander or planer to remove the convex material. Less risk but more work.
I had the same problem with a new board. Once warped, I saturated it on both sides with mineral oil, convex side was facing my counter, placed wax paper over that to give a semi-porous barrier, then plastic wrap on the top, and layered books on it. Then left it on a flat surface and it amazingly flattened out. I now store it completely flat and it has been fine.
I have accidentally warped many of my own cutting boards. I put the cutting board over a steaming pot, with the bent out part sticking in towards the pot. It reheats the board and the board starts warping in the opposite direction. I take it off when it's straight. Works every time.
We buy bamboo chopping boards and having a little kid means don't have the time to properly wash them by hand or oil them with food grade mineral oil. Our boards just go into the dishwasher like all the other dishes. This causes them to curve in the direction of the spray.
What I found is that if you reverse the board (back face to the dishwasher spray), the next time around it goes into the dishwasher it would curve the other way and straighten out. This is probably terrible for the board, but it does fix the curving problem.
Might want to give it a try, if all other options here fail.
I had one that was warped pretty bad. It eventually righted itself by laying it 'flat' with the convex side up over a pot after soaking/washing it thoroughly, this allowed it to dry more evenly with air flowing underneath and it knew what to do.
I did not use direct heat, but it was there for a couple days next to the other 3 burners
I did not use any weights
I did not steam
the pot was completely empty the whole time, with nothing in it but cycling air.
The board did not cover the pot completely, allowing air to circulate around it.
I repeated this process a couple times to get it ~96.2% back to it's original 'flatness'
If you have electric burners (coils) (probably easier/safer than gas for this purpose) then there are many less than safe, supervision required, ways to accelerate the process mine went through. Of course you could also rig something in the oven. Note that accelerating the process could also cause it to warp more. Clearly this phenomenon was not well documented, but I wanted to let people know it's possible.