Here is what I would do:
1) Camp deep freeze, then invite him for dinner one night.
2) Re-home, but only if you are very clear as to his aggressive behavior. I would feel terrible if my re-homed rooster harmed a child.
3) (Re)Train the rooster if you have the time and/or energy, with the expectation that you might be back to 1) or 2) in the end anyway.
One thing I did to make my life easier with my chickens is that I can lock my chickens up in their coop when I need to do maintenance in the chicken run. Nobody sneaking up behind me or trying to escape that way. Similarly, I can lock the chickens out of the coop when they are in the chicken run, and do whatever chores I need to do in the coop, knowing that no chickens will be looking for the door and freedom. Finally, I have an outside access door to gather eggs which is basically safe from both the coop and the run. I know lots of people have that kind of setup, but I think it's worth repeating because it makes life with chickens so much easier.
Because of predator concerns, I do not let my chickens free range. The advantage to me is that I always have control over where the chickens are. Although not funny, I was laughing to read that you ended up throwing eggs at your rooster. I would suggest that you find a way to collect your eggs without having to worry about this rooster, or any future rooster, sneaking up behind you.
I'll be reading this thread to see how things turn out for you. Good luck.