I would look at the drivers which exist for LED diplays. Typically these are modular, and drive (say) some number of 8x8 grids of multiplexed LEDs.
Those are for flat panels, so what you'd need to do is alter the number of panels in each row to make it follow a series of smaller circumference cylinders, or start omitting columns.
Rather than using an existing LED grid, you would want to wire up your own with the columns slightly wider apart at one end than the other so they stack up to form a cone rather than a cylinder.
You would have to map your spherical image onto the oddly dimensioned grid, and this may take a little software effort.
I think it might cost you thousands, but not tens of thousands.