holy crapola! $20 per letter for all your schools?! So we're talking $400+?! Dang. That's a lot of $$! I really do think it's fair for you to request that they send the letters directly to the schools. I know what you're saying that you don't want to inconvenience them, but put yourself in their shoes -- would you be bothered to print the same piece of paper 10x, fold it up, and put it into an addressed, stamped envelop? 2 minutes, max! If they wrote you letters of recommendation, they obviously think you're a great, strong candidate and are willing to do this minor thing to help you out!! Don't sweat it.
Aside to everyone: Be sure to write your letterwriters a thank-you note!! I actually received a thank-you note from one of my professors thanking me for thanking him! Apparently not many students do this, which blows my mind!!