First of all, your set-up looks just fine. How many gpm's is that pump? You don't want too many or you will create too much runoff. I would recommend that you have jumper cables handy - in case the battery dies.
For anyone that has never washed a roof with what I call "3 dimensional fungus", you must warn the homeowner that, even though you will "kill" it, it will still be there! Moss/lichen have roots, unlike the black streaks of algae that are usually the reason the phone rings, and will turn white - but it can take several rains to rinse the roof clean. The homeowner must be prepared for this, or they will not be happy! I always explain the "roots" issue as the reason not to use any pressure to coax the stuff off the roof. That roof will look great, but in all likelihood, it will look worse at first.
This roof does not have gutters - at least not in front - so you will want to not only flood the shrubs with water, but cover them when spraying the roof. Your roof mix is toxic to plant life - and the hotter the mix (and the hotter the air temp too!) the faster the damage will be done. If there are any downspouts, you can zip-tie a trash bag to the end to catch runoff. (There is a product you can buy that will neutralize the chlorine, and I'll post it when I remember. LOL) Remember, any residue will runoff the next morning if there is a heavy dew, so especially on houses without gutters, you have to take extra precautions.
Finally (?), safety. Roofs are slippery when wet. Even more so when coated with roof wash mix and even MORE slippery when there is 3 dimensional fungus + steep pitch. Please be safe. Also, a respirator will come in handy - especially on really hot days. The fumes can be pretty bad. I also highly recommend a ladder stabilizer. Not only will this keep the ladder in position, it will prevent you from damaging the gutters/shingles.
Be safe, make some money!
John
P.S. My phone is always on!