In all my years of plumbing, I've never done it the other two ways.
On the West Coast, they would laugh.
Here, we expect every fixture to be vented above the trap arm, not below.
I would be looking at fitting in a way to run vents, even if it's through cabinets. In many exposed structures, they still plumb to code, it's just that they go with it and find a way to make it look intentional.