I've found two products that seem to fit these specs: Wet&Forget, and Seal It Green Tile Roof Wash. Anyone have experience with either?
1) Wet&Forget is more widely distributed -- available from Home Depot (online), Amazon, and apparently from Costco (can't find it on their web site but other evidence says they carry it). Reviews on HD and Amazon are mostly very positive. Works slowly but that's fine with us. Would probably require 4 gallons for this house, lowest price I've seen is $33, so about $132.
2) Seal It Green seems to be available only direct from the manufacturer. Makes strong non-toxic claims but does say to pressure wash after applying and allowing to dry, which I'd rather not. Cannot find any reviews. Would probably require 10 pounds, for $125 plus perhaps $10 shipping. (It's one of these web sites that won't tell you the shipping cost without entering all your personal details, grrr.)