Is it appropriate to ask for double my current salary on these grounds?
Double your salary? Probably not. In fact, almost certainly not. Software engineering, like most of engineering, is rather egalitarian. In almost every field in engineering, the top outperform the bottom by a lot more than your factor of three or four. Pay is not commensurate with that huge variation in performance. People who can't program their way out of a wet paper bag are paid almost as much as you. People who can program even better than you are paid only a bit more than you are. That's life.
To make twice your already nice salary of $120K/year, you need to do something beyond programming. If you stay where you are, you might eventually see that 100% pay raise, but only over the course of many years. Another option is to climb the ladder and become a manager. An even more lucrative (but much more risky) option is to become an entrepreneur and start your own business.
A third option: Look for something other than money in your job. If you're as good as you think you are, look for and ask for the most challenging assignments. You'll be paid more than your mindless cohorts (but not double), you'll work harder than your mindless cohorts, but your mindless cohorts will be doing mindless work. Your work will be fun and challenging. Even better, find ways to create your own work. You might get nice bonuses for that.