If your engine runs fine as long as you prime the fuel hose bulb, the engine is starving for fuel. You need to start to examine all the fuel components, systems on the engine. Such as: Make sure you have a genuine (black) 5/16" factory fuel hose from the tank. Some of the older grey ones have problems with the ethanol-it breaks down the inner clear liner. Also, some of the ball valves in the hose bulbs fail, causing suction problem. After all this, I'm not sure that you have ever had the carbs apart for inspection and cleaning. Dried fuel inside a carb won't just dissolve when you run new fuel thru it. You need to use a special carb cleaner, such as a Gumout type product. You have to pull all the jets out (high speed and idles) and visually inspect them for debris, or bits of deteriorated fuel hose, etc. Some times main jets may not be screwed into the bowls fully. Check them for position when you pull them out. Make sure the floats actually will float in gas and that they pivot easily. (They should be ok, but just check.) Your 79 carbs are nearly identical to the 85 carbs, but without the mid range jets. (Not a problem.)
