Leslie, first you'll need to be 100% sure neither of these walls is load-bearing; being 90° to each other, one of them COULD be bearing.
The next issue is what's inside those walls; wiring, plumbing & any ductwork could be an issue.
Bearing or not, one option you would have would be to create large "windows" in the walls, leaving a header beam across the ceiling line, and retaining full-height columns at each end. This would relieve you of any ceiling work.
Being a smooth painted ceiling, if the walls are truly petitions rather than bearing, and free of service runs, you could remove the existing walls entirely & patch in the voids left in the ceiling with little problem.
I'd see no reason to not make use of the existing framing instead of starting from scratch, but I would plan to remove all existing drywall from them to allow for some additional framing to be added to stiffen the new half-walls & counters.
Good luck & have the load bearing & service run issues checked out before opening things up.