Here are a few things that you can do. First, if you can get your slabs a little ways out from the pith / juvenile wood where the rings are small arcs when viewed from the end-gran. Cupping is a caused by the 2-1 ratio between tangental and radial shrinkage around an arc. So, if you could rip right through the pith, the slabs on either side would be mostly QS and stay flat, until near the pith, where the arcs are about the size of a tennis ball, then there will be more of a kink than a cup. As you move on out, the cup will become less.
I believe the kiln experts can manage to get a flat set in the process, but I don't think it would be permanent air drying.
One thing I do with wide slabs is to incorporate some of the under-structure into the top, by routing a big T slot into the underside, which bridges between legs or apron parts. The wings of the T are waxed to allow seasonal movement, and support for a seam, which may or may not be a glueline. The slot doesn't go all the way to the edges, unless it was a single board, then the slot would only be open for assembly, then filled on the side where it slid in from.
If you started with a slab too thick to clamp and hold the cup out, you can kerf the underside with a series of kerf that allow the remainder to be thin enough that the T can hold it flat. Choosing a good strong tight grain T member is good, but even that can be improved by running long screws down from the top, about every 6" apart to resist splitting can help.
I've never had this fail, and it WILL keep it flat as it was when constructed.