This is only somewhat related.

I have in the past moistened the cupped side of a plank to flatten it out. Then added gussets to keep it flat.

How thick is it?

Can you refinish the top?

I think that furniture items and cabinetry are more relavent to this article.

Michael or Mike?

Since the top is only 3/4 you should be able to get it flat and keep it flat with the cauls only. If you can take the top off, you could clamp it flat with temporary cauls and route the bottom for permanent sliding dovetailed cauls. Forget the tent, dehumidifier and even putting the finish on the bottom side. As long as the sliding dovetails are a good fit the top will stay flat. JMO

Eiji

It will be even easier than you suggest since the thicker band around the perimeter prohibits sliding dovetails. It'll just be screwed on cauls.

I am started to reconsider adding finish to the bottom since that will delay adding the cauls, but, I think the owner is set on adding it.

qoute from tvgordon....
I just read an interesting article in the July 08 issue of Woodshop News.  It was written by
Bob Flexner and in it he says that the need to finish both sides of a board is a myth.
quote from michael......
One of my current projects is to flatten a large slab table that is only finished on the top.
(Slab as in a large board that sits on cabinets rather than having an apron and legs)
It is humid here now and the finished side is cupped. I think I'm going to have to build a plastic tent around it and put a dehumidifier in there to try and flatten it.
Do you think that will help?
Whether it does or not I'm going to seal the bottom with a couple of coats of something and add cauls to keep it flat.
The table I'm working on is maple, 44" wide and 3/4" thick with a 1 1/4" molded band all around dovetailed in the ends.
The table moves a good 3/4" in width through the seasons and the finish in great condition and must be preserved.
The guy that made this table is one of the best makers of Windsor chairs and also has a lot of experience restoring valuable antiques. He would agree completely with Flexner. However, the wood he used on this table apparently wasn't completely seasoned and since the slab isn't braced by any structure I think the decision to leave the bottom unsealed was a mistake.
I think it's best to seal all surfaces with the same material and at the same time if possible. This of course would add a lot of cost to the piece so best isn't always the right choice.


Allow me to interject here........

If a piece is secured by a structural frame I could see skipping the step of finishing it all around.
(this would also depend upon how it is secured, but that could be another post)

If it is not secured, such as a slab as Micheal's client or a cabinet door I personally would always finish the unseen side.
If it's not seen, it doesn't mean that it is not absorbing moisture from the surroundings, even on a closed door cabinet.
(Keep in mind that I came into woodworking from being a finisher for years first, and working on a lot of antiques at that)

I would disagree with Flexner if he is using that as a blanket statement (having not read said article)

Micheal, your assumption was correct......
Now with respect to your project, my first course of action would be to sand the bottom surface first - to open the wood cells.
(I don't believe you mentioned how many years, since it being made) My second step would be to apply a couple of coats of a diluted finish of whatever your guess would be of what was applied on top. (waiting between each coat).....to allow it to really absorb within the maple (esp because it is such a dense wood) I would then apply a thicker coat and wait.

Something is going to move.

Flipping it, against the cup with a two by four on edge running across the width, clamped at either end to the
(mft table below?) as the finish is curing (with some wax paper between the 2 by 4 and the finish) could help.

I'm not so sure if adding the cauls without sealing it first, at this stage would be a complete success over time.
(you might have him sign a waiver, if you do go that route)

anyhow, my 2 cents before my morning coffee,
Roger

hmm, any chance to see some photos?

p.s.
qoute by underused.....
I've also put a warped board out on damp grass in the morning, and had success flattening it back.
......that could work on a board that is not finished on the side not hitting the grass, if you do that on a board that already has a finish on the otherside - such as Michael's, I believe you could make it worse. Remember, it was excess moisture from the unsealed side which stared this mess in the first place.

What Flexner wrote in the article is true during equilibrium conditions (when any absorption, evaporation of moisture from both top and bottom has ceased). Here in New England, there can be wild swings of short duration in relative humidity. For Michaels table top, with its 3/4 inch variation, an unfinished bottom would be growing and shrinking more rapidly during these transition times causing temporary bowing and cupping stresses until an equilibrium is reached.

I don't know what the best compromise is, but there may be some benefit to sealing both sides of a table top.