Beginning to get the feeling that removing obstacles to von Karman-like swirling flow isn't the answer. You have to shut down the centrifugal pump the flow entails.
How to do that without an external shroud?
To make the top without the core like in the curtain ring tops of Ortwin is one way, I would like to make a top in that way one day.
The spokes should be very thin, it is not very easy to make a precision top in this way.
Maybe the spokes could be directed not towards the center of the top but could be set obliquely, to better accommodate the flow of the air, (photo below).
Another way could be to look for surfaces slippery for the air, (to reduce skin friction), but I am not sure if this is possible in our case.
I read that it has been found that the surfaces of feathers, (if memory serves), or the skin of the wings of bats, have less air drag than simple smooth surfaces.
There are aerodynamic fabrics, the textures of which reduce the air drag;
they are used by athletes in sports where reducing the air drag is an advantage, like skiing or cycling.
The problem is that, as far as I know, (which is very little), some speed is necessary for these fabrics to work properly, and probably spinning tops spin too slowly. These things can be tested, in any case.