I own a 100yr old house, hot water radiators, all the radiators were busted when I bought it because it wasn't properly winterized. All the pros tried to get me to replace it with forced furnace. I ended up buying used steam radiators and doing everything myself for the fraction of the cost and it's been 10 yrs. You're absolute correct, draw a diagram, being at first principles and it's easy to reason about the system.