Kerfing is what I saw with the plywood at the grocery store. The arches were actually part of the remodel they are going through and they were outside about 10-feet off the ground (something for people to walk through as if they were doors). This is the method I used to create the rounded corners on my cardboard control panel mock-up. I anticipated this would probably take a lot more effort and thought with wood, but I guess I didn't know just how much.
I've thought about a couple of ideas and these don't seem too bad from my point of view, though, again, I haven't a clue how hard it would be.
Option 1
Instead of kerfing, I could cut very explicit triangle cuts as far into the plywood as possible without cutting through. Then I could bend the outer most "ply" to my liking. The downside is that although it seems like it would be structurally sound, I would still end up with multiple flat faces in a faux curve.
Option 2
I could buy a couple of big blocks of oak from one of the specialty stores here in town and cut my curve to size as necessary. The downside to this is the amount of wasted wood for the cut and the REALLY expensive prices for blocks like I'm talking about.
Option 3
Block the curve out as much as is possible, fill with wood filer or fiberglass filer, then apply a sheet of oak laminate. The downside of this is that I don't even know if you can stain a sheet of laminate, plus, the grain would be significantly different from the oak plywood.
None of these options really appeal to me. I'll likely spend more time on getting these curves right than I would building and wiring the entire control panel.