Iratior: As an exercise, you could hit the bass with the thumb. Somehow (well, it's not very strange when you think about it), if you know where the thumb is, you know where the rest of the hand is, so to say. So if you are practise to hit the bass with the thumb, it will be loads and loads easier to hit it later, since the hand knows where the key is.
N-something: Well, as I said, I don't do big arm motions when I play for real, just when I pratice Chopin etudes and pieces like that.
Maybe I get this wrong, but it seems that you assume that I can't play the piano a single bit, and that I probably have no technique at all? That "on the spot" really doesn't work. I have attended many masterclasses with quite famous pianists and pedagogues, and none of them has ever complained about my arm motions. In fact, they have said some very nice things about me (except for one french teacher, for whom I played Debussy.. Don't do that if you ever have the chance) being able to change tone and articulation very quickly. That is all thanks to the arm motions. Being on the key makes it much more difficult, for me and everyone I know, to change the tone (and even have a tone)...