Not trying to be a hard A**,..but there is no need to have to be "Clawing" to put a roof cleaning rig together. Either buy one pre-made or buy a an air pump or 12V and go to work. It's that time of year. I understand maybe the money isn't there,..but you have to figure that out,..and quick. Go to Kleenrite.com and buy an air pump for little over $100.00 if you want air.
If you want 12V go to one of the vendors here or Tractor Supply and buy one. Many of us started out using garden hose as the supply hose. There's lot's of easy and economical ways to put a roof rig together,..and the work you get will pay for a more updated rig. I did alot of roofs with a pump sprayer back around 2004-2005,..(Not recommending that,..but it will give you a paycheck)
I even did roofs with a a 1" Homelite centrifugal pump,..absolutely the wrong kind of pump Ha,Ha,,..but I did make money with it. I didn't even have a by-pass on it,..I would just shut the "wand" off and it would just swell the garden hose extra big and the engine would sit there running with a load on it from trying to pump,...one day it started leaking at the seals,..then I went to a roller pump,..which worked very well and was my most "normal" system to date at that point. Rollers are obsolete for roof cleaning now.
You have something I didn't have,..you have a wealth of information right in front of,..don't make it harder than it is. Because I had no internet I didn't even know roof cleaning was an actual service,..so I was just winging it,
I provided a link to a decent little money making pump,..it's 3/8",..same size as an All-Flo that many of us have used and still use. I have the 1/2" Versa-Matic and it works great. But if I were on a budget this 3/8" is the way to go for air.
https://www.kleen-ritecorp.com/p-5442-versa-matic-e8pp6xpp9-38-pump-polyproplene-body-santoprene-diaphragm.aspx
Jeff