I'm curious if the lack of heat in the lightrays will ruin the immersion of sunlight? Perhaps couple this with an IR heatlamp to add the real feel of sunrays hitting your skin?
For full immersion you would also want a number of different light sources since leds are have very narrow spectra.
Mixing violets and greens makes the spectral curve closer to that of sunlight.
Again, without seeing it in person there is no way to know how much impact this has.
Using a parabolic reflector however is the only way to go since you will not get diffraction or blocking of wavelengths.
[0] Applied Photovoltaics, Earthscan Publications, 2007: http://www.eng.uc.edu/~beaucag/Classes/SolarPowerForAfrica/B...