it's usually about how much energy your setup takes to recapture turbulence into useful energy after the first spin, and it's a tight-rope act trying to figure that stuff out.

So yes, I imagine you could, but at some point those hydrodynamic gains run into the physics problem of spinning mass even if you can walk the turbulence tight-rope.

I wonder how contra-rotating schemes compare to something like PBCF?

https://www.youtube.com/watch?v=a8PjWSeLUzY

It seems like it should achieve almost the same de-vortex efficiency gains, but without all that added mechanical complexity, skin drag, and underwater noise (PBCF is actually quieter than having no fuel-saving device).

Honestly I'm surprised Sharrow doesn't already use it on their regular toroidal propellers. I notice a lot of hub vortex in their underwater videos...

What would be the point? Contra-rotation has limited use as it is. In this case the stated reason is to ensure the axial flow has no energy wasted in twisting (though this can also be achieved with a stator) - in any case two stages are enough for this. The other main use is dissipating more power when you are up against some sort of limit on prop size, but this is not a common problem underwater.