Your plan sounds reasonable, as long as you understand that once the algae is dead, you're still going to have a pretty big chlorine demand to overcome due to the ammonia in the algaecide.

Does your neighbor have a sand or cartridge filter? If it's a cart, then it's going to clog very quickly, and the only solution I know is to keep a couple of them rinsed and ready to be switched out. If it's sand, it will still clog, but not as quickly and is a quicker job to backwash. You want to backwash a sand filter when the pressure rises 6-8 psi over "clean" pressure, since a dirty sand filter cleans better than a clean one does.

About the Polaris--unless your neighbor has the silt bag, and unless it's much better at the smaller stuff than the regular bag, I would leave it off and save the electricity. My Polaris doesn't do worth a flip when it comes to small stuff like algae. Better to kill it off and then filter or vac to waste.