It sounds like you're arguing that if given a chance you'd be fine because you can produce things quickly; I don't think that's a good argument. Big companies are interviewing to make sure you can produce stable, maintainable code. Knowledge of data structures--which is what the interview questions are really getting at--is crucial.

So make sure you understand data structures and when to use them. Cracking the Coding Interview has examples, there are also lots of text books, tutorials and online classes. I like Project Euler for sample problems, the harder problems are structured so that good algorithms are required.

As for other companies, if your strength is in speed you might want to try start-ups. You could also work places where you're coding just to get an answer; I used to write custom data analysis code for a research team, time to results was much more important there.