The condition that does not need to hold is the shutter speed. With 3 stops of ND filters you could get the shutter speed down to 1/200.
I don't know whether this would be a better solution than reflectors, but it would at least be possible.
Another good option is larger diffusion panels, as used in motion pictures.
These are large diffusion screens placed between the sun and the subject to negate deeps shadows in that the OP seems to be wants to mittigate.
But personally I would just use the reflectors and make the dance a two step, not a complicated tango.