Just went through one of my boys 306a. Had something similar going on. The pump side of the carb looked great at first and the needle side looked great too except the needle cone was very slightly discolored if you held it to the light just right. Ended up using a new needle, diaphram and gasket, and a new pump and gasket. The fuel lines looked good but the tank side looked to have been shortened, so I pulled the tank top and added a new longer hose and made sure the filter was CLEAN clean with carb cleaner and air.If the filter is rock hard they won't pass much fuel. Ended up adding a new tank to carb line after finding tiny cracks when I put it back on the barb. I did check the reed valves and took some gunk off them. What I found after that was that the low speed jetting was very, very sensitive. 1/16th of a turn would make a difference between loading up at idle and acting correctly. The jet screws shouldn't feel loose if the springs are good unless maybe someone stripped them partially. Speeding up and dying sounds like fuel starvation, which is pretty much what ours was doing. I think it was the pump even though it was pliable and not rippled looking. It's a cheap thing to replace and it's right there on top and easy to get to. Old fuel lines that aren't gummy worms can still have leaks too.
