This sounds like the exact problem I was hoping to solve with Armory's signature blocks (and message signing just implemented in Satoshi 0.6.0).  The only requirement is that the user's first ever deposit is with an address they exclusively own.  All future deposits to their account can be through any means whatsoever.

Require the user to use one of their own addresses, X, for the very first deposit even if it's just 0.001 BTC.  After that, any interaction they have with the casino must be through signature blocks, signed by X.  ("I would like to cashout 12 BTC to the following address ... ")_signed_by_X.  This is a guarantee that the same person who originally funded the account is the person who is sending you the message -- and that the message can't be altered on the way.  After that first deposit, they can "refill" their account however they want (green addresses, friends, other addresses).  Only the first one matters.

You can make all interaction between customer and casino as anonymous as Bitcoin itself -- they would not even need a login/password/email/anything.  They only communicate through signature blocks on your webpage or email, and your software can easily check that the signature on the message matches X.  Right now it would require manually creating the sig blocks, but it could eventually be a capability somehow integrated with a client or browser, just for this purpose.  You could initiate SSL connections between casino and customer using public key X.  

Of course, if you don't want pure anonymity, you can require more information to open an account, but there's a ton of flexibility with this method.