My Builder suggested sloping (with a beam at the room transition point) it if I didn't want a typical "boxy" transition step-up.

Sloping what? All your ceilings are flat?

Slope what gradually? The kitchen ceiling?

I'd advise against the slope. Unless it's part of a four sided theme (like a trey ceiling) in the living room it will look awkward and forced. Slope ceilings, IMO, should only be used where they are mirroring the roof slope. (i.e. around dormers, or in true vaults.)

Probably the best solution visually, as well as economically, is to frame a wide opening with head at 8'-0" between kitchen ceiling and living room ceiling. This will accomodate your cabinet needs and provide a logical spatial transition between the two rooms.

A "sloping ceiling" is ridiculous, unless you have other such things elsewhere in your house. Don't ask your builder for any further recommendations which are visual.

Good luck on your project.

What Virgil said. This slope will be so shallow it will just be weird.