re: Table top rehab

What direction is it warped -- side to side or lengthwise?  The warping along with the glued on battens is probably what caused the failure.  

A trick that I have used to flatten warped panels and table tops is to lay it on the lawn in the sun convex side up.  The panel will absorb a little bit of moisture from the lawn and the sun will dry the top a little flattening the panel.   It happens pretty quickly so check it every 10 minutes or you may come out to find that it has warped in the opposite direction.  Take it in and lean it against a wall or bench or flat with some thin strips under it so that air can flow around both sides.  Let it sit for a day or so and check it again to see if it rewarped.  You can try  this several times and see if it will stabilize.  

You can try to use battens, either original ones or some angle iron or channel to pull it flat but again, you need to use  elongated holes with plenty of screws to force it down.  You may have to do this and the glue up all at once.  

BTW, is this solid wood or some sort of particle board or MDF core with veneer.  It looks like wood but it is hard to tell for sure from the photos.