I'm afraid I don't think you can look for a reputable service for that function. If your funds are going to be used for gambling, non-custodial wallets are the only way to go. For the sole reason that they are non-custodial, hence you wallet doesn't have a say on what you can and what you can not do with your money.

If you ever find an alternative to BitGo that allows your funds to be used for gambling, I think it won't be that way for long.