No posts at the corners, right?

Are you willing to patch or redo the floor? To panel the backs of the cabinets with a veneer? To do the electrical work to put the outlets on the sides of the cabinets? To replace the countertops? If you want an overhang, to create the structural support for that to happen?

Are you handy enough to do all of that DIY? Or do you have about 1-2K to hire it all done by a good finish carpenter, electrician, and counter fabricator?

I wonder if there is wood flooring under the short walls. Would be an expensive job if there isn't floor there now and you can't find flooring to match. I can see why you'd like it to come down though. Would really open up the space.

The flooring was installed after the surround was framed in. The flooring will be replaced due to a dishwasher leak so that's why we're looking at adjusting the island. Starting to look like a can of worms though.

Definitely a can of worms, but now is the time to tackle the challenge if you have to replace the floor anyway. Your cabinets and counters look nice, but that space looks really outdated and will likely have an impact on resale if that is a potential concern.

You could eliminate the "L" and change it to an island, reusing the same cabinets - minus the corner cabinet - and make it more in tune with current kitchens. Replace with a coordinating or contrasting counter.