I think making it flat does not sound all that likely to work, you normally need to go in the opposite direction. And normally I just replicate the condition that caused the problem, but in reverse. I would examine the curve and mark it on a caul, then just clamp in the opposite direction. It probably won't take very long to get back to flat. The more time you have though, to check for backsliding and make corrections, the better.
Water can affect the dimensional purity of the panel. What it should not do is slip the glue, or the lignin. It will reduce the tensile fiber strength of the wood, which isn't really a bonus. So I don't think you will get anything out of wetting the wood.
There are activities like archery, where we just hand straighten stuff all the time, and it stays straight, and works great until the next tweak sends it off. This isn't a technology that all woodworkers are familiar with, but it works, is normally what caused the problem bend in the first place, and correcting it does not require doing anything more fancy than counter bending.