I must say that yours is the most appropriate way of explanation the verb "tackle". Explaining something the way that it could meet the different needs takes certain skills that you sir definitely have it. I had also had a longtime issue in figuring out the exact meaning of the verb. I did question alot, None of the dictionaries on the internet properly define the verb rather than explaing its figurative sense - "to try to deal with" - expecting a learner would sort something out of it. But what we need actually is to find out where the hell that figurative sense comes out, how it came into use, the relation between literal and figurative meanings, how both these two are relevant? All these clues I've mentioned above are esential for us to conceive the real meaning, the feeling the verb actually conveys, an impression the writer wants to give by using it.tackle: jump at quickly and throw to the ground with force, also, attack a problem.
handle: manage quietly.
In American football, you tackle your opponent, run at him so hard you knock him, and the ball he's running with, right to the ground.