I have subbed out a ton of custom made "Formica" tops over the years, as a homebuilder. Many tops were significantly larger than yours, and fabricated on site. They were always 3/4 MDF, with another layer of 3/4 MDF strips attached to the bottom, for stiffeners and to create the appearance of a "thicker" top. The stiffeners are attached with yellow glue and 1/4" crown air staples. I have never had issues with tops bowing or sagging.
Before you go any further I would place the top on a flat surface, block the ends up on some 3/4" scraps and place some weight in the center to straighten the bow. Leave I like this, at least overnight. I once had a painter who was some kind of sorcerer, when it came to getting bows out of doors. He would put them on horses, shim at different locations, pile weight here and there, and leave them in the sun for a while. It usually worked, somehow, LOL.