Are there any mills who have effectively produced RoHS compliant material that does not end up with white stain resembling white rust? (galvanized coil)
Yes. Nippon Steel offers ZINKOTE®21 (electrogalv) and DURGRIP21 (hot-dipped galv). JFE calls their products Eco-Frontier. I'm sure there are others. The two links below provide additional information on these products.