Interesting warping problem and question on how to fix?

Suggestions:
1. Wet the concave sides and allow to dry on a flat surface.  Crap shoot at best.
2.  Trash that junk oak and make them a nice oak table out of WHITE oak, but remember why  the red stuff is called junk.  Very short in the stability department, even when finished.
Note to subconscious:  Even if you get it flat by No.1, it'll likely warp/twist/belly again with seasonal change.

I have no idea what the table design looks like, but you can flatten those tops by screwing battens on underneath. Depending on whether the surface is concave or convex, you may need to crown the battens enough that you can dial in the flatness by pulling the top down with screws.

Ellis

I'll agree that the simplest solution is to use different boards. 

But if these were mine and I wanted to fix it, and assuming they are strait in the long grain direction and cupped in the short grain direction, and assuming I have some extra width to play with, I might also try:

Bandsaw apart a glue line somewhere near the middle, or at two joints, re-joint the edges, and reglue. I would probably have to re-plane them flat and lose some thickness, but not 3/8".

And yes, I'd add some battens if the design allows it.

Were they touching each other while leaning against the wall? Were they both exposed evenly to the conditioned air?  Was the same side of each facing the wall?  Seems to me they must have dried unevenly in the conditioned space. With even drying conditions hopefully they will at least match.

After all the meticulous milling and clamping, leaning on the wall in the conditioned space was a random haphazard event.  I took them out into the hall and leaned them on the wall.  Then I went back and got them.  I paid no attention to putting them there except to make sure they had an inch or two of air space around them.  I have no idea if the top side was "in" or "out".    Did not check them when I went back to get them except that I noticed they were curved but thought it was my progressive lenses playing tricks on me until I laid them in place.
Last night I measured the "step" between them and it was .22" and this morning it was .19".  This is back in the shop where they were made.
I am at a loss.  Reluctant to wet the concave side because that seems like a temporary fix. Considered using a heat gun gently on the convex side.  Thought about slots in the underside.  Got some stiffener bars left over from another project but....?

I have some local Big-leaf Maple that was supposed to be kiln-dried. Doing tests on one board (guitar faces) I worked down the board from just shy of 1-1/2 inch to just over 3/4" in several planings over a year-long operation. It never flattened but rather returned to its original warp. These boards are just under 12" wide to clear a 12-inch planer. 

I tried every trick and am now redesigning the project, since I am adamant to use local species.

Not only do I use local species, sometimes its even closer to home.  My white oak came from a huge tree that fell on a rental house I own, the red oak came from a tree in my front yard that died,  and the walnut, cherry, and poplar came off the family farm.

I fiddled with the panels for the table top, wetting the concave side and putting them into the sun on the convex side and they flattened to within a 1/16" of each other.  If they stay that good, I will sand them into submission.  I will put dominoes into  the edges to force them to remain in plane with each other.

If you removed more material from one side than you did from the other the differential could have caused this problem.  The fact that the curve seems to be reducing is a good thing.  I would give the pieces a few more days in your shop and see how they behave.  I've made a lot of things from Red Oak including some glued up 24" wide panels that have remained flat during construction and use.

Warping of large flat panel glue-ups can be frustrating to deal with. Here are a few suggestions:

• Adding weight on top can help flatten them out over time if the warp isn't too severe. Place boards, weights, etc evenly to apply downward force.

• You can try clamping them concave side up and letting sit clamped for a day or two and see if they relax flatter.

• If they don't flatten with weight/clamps, you may need to cut the panels into strips, joint/plane flat, and re-glue into panels.

• When re-gluing, make sure moisture content is equalized and use proper clamping cauls to apply even pressure.

• Consider adding breadboard ends to help keep the edges flat and reduce future warping.

• Adding an apron around the bottom helps stabilize a panel long-term.

• Maintaining similar conditions from construction through installation reduces additional movement.

With time and patience, they may flatten enough for your needs, but be prepared for more invasive options. In the future, over-sizing the panels initially provides room to mill them flat after.