First off, I really like your lottery! I even tried for a while to win the jackpot! But lost, dang it!
I was thinking of your site today after that post and it got me thinking. You could change a few things. It would still be simple, yet eliminate any question of cheating. It would also make it more fun!!
Here's what I'd do:
-don't change the send to address / payment address part. It's very simple and elegant! BUT, when you ask if the address is yours just say "1KLk...aPw" with a good portion missing.
-when they first register they are given a link. This link would be betcoin.eu/(theirpaymentaddress) and they are told to remember it or how to figure out what it is if they lose it. If someone figures someones out, it not a huge deal since all they can do is make their picks and NOT change where its going
-that page will be their pick a number page. It would be like your incoming payment tx pages but it would be a list with all the transactions for the sending address.
-once a payment is verified a link will appear letting the person make a pick. When they click it it opens a new page.
-now they are on a page where they pick a number 1-500. You could make it look all cool with graphics or having a 3-digit wheel they spin to select or something. Underneath is a hash. This is the hash of a list of 1-500 listing what each number is. 1.2x, 2x, lose, and one with the jackpot. They then pick a number and click submit. It then loads a page showing the data with random data as well and the same hash of all the data. Then they click next and it goes back to the "pick a number page".
-they get to pick for each payment
-MORE FUN as the user feels like they are more in control of the outcome
-impossible for people to accuse you of cheating
-dealing with the randomness is more simple because people are actually determining the outcome and not a random number
You could even have it where no selection after 2 hours or something will have one picked for them.
I REALLY hope you do something similar. I just kind of hope you don't as I may get addicted to your game!