Missy, have you tried plain old chlorine bleach (Clorox or similar)? This is usually a pretty good mildew/algae killer. The problem is that, while you can spray it on, it helps to scrub it off after it has had time to work.
If you fall off the slippery roof, the $3500 will seem pretty cheap so be very careful if you decide to try this. Remember that water and the algae will make the slate a lot slicker than it is when it is dry. Personally, I would not consider this on a roof over a one story high building and not then if the roof pitch was pretty steep. BE CAREFUL.