I was frozen three times, the first two I sent them the email (filled out the form) and they let me return both times (think I was scammed the first time, a long time ago, and the second I signed on at my friend's house and they thought someone was stealing my account so they froze it for safety reasons). The third time I just stopped playing for a while because that annoyed me (I had too many accounts, apparently.. funny thing is that they didn't freeze the one that was worth the most..)
Maybe you could use two computers. Open the game, then type the numbers in the other computer (into a solver), and then the instant that loads, type it into the computer with the game open. I could easily see that being done in under 30 seconds. Think about the time you save from switching windows...