I have java moss in a high light tank and it grows like algae, very fine and very green. I do not add fertilizers or anything to the tank, only 36 watts of 6500K compact fluorescent overan 8 gallon tank. I try to keep green water in this tankso the spectrum and intensity is diminished by the time the light gets down the water column to the moss.
My other tanks are pretty standard 2 watts per gallon, the java moss and java ferns both grow quite well in medium light, well fertilized CO2 injected tanks.
IME, high light is fine so long as you have some hornwort, duckweed, or other floating plants to reduce the intensity on the java plants. Try to keep the java plants deep in the tank and not right at the surface, this also helps cut the light intensity as well.