Before you rip up your table top, there are a few things you can consider.
Solid table tops quite often will cup slightly until fastened properly,
taking into account grain direction and movement.
I know a 3/4 inch cup over the width of your top can look discouraging, but
don't get too upset.
There a host of different approaches to your challenge. Consider how you
are going to fasten it to your table structure. Can it be coaxed flat by
your fastening method?
If not, there are a few things to consider before ripping it. Can sliding
dovetails, or dados with a rigid piece of stock screwed (with elongated
holes for movement) be incorporated along the width of the underside of the
Since the design is for yourself (not a paying customer with an approved
design), a simple breadboard end design , is not terribly difficult to
incorporate and minimizes cupping...
...cupping is always a threat, in solid wood, unless you engineer a method
to prevent it, no matter how well or technically correct you joint it.
Cheers, and good luck.