so far i would be inclined to go for some injector cleaner or possibly even some 2 stroke oil as i think it is sounding more like an injector issue . the primer being soft when running i think is normal as fuel is constantly being sucked thru it . i think it could be a sticky valve issue but i think you would hear that . fitting a lift pump might confuse or disguise the problem , so i would hold off on that until the problem i found and sorted .