I am depositing crypto as well sometimes binance restricts transaction to bc wallet. And also sometimes to avoid fee I use fiat.
There should be support behind every problem
What's the issue if you use your own address instead of using Binance to deposit and withdraw? It does mean you have to use a non-custodial wallet to send and receive funds from the gambling sites. If you can afford it, then I would prefer purchasing a hardware wallet to secure your funds.
Binance would restrict your accounts when related to the gambling sites or mixers. Simply buy your desired crypto from Binance or any other exchange using P2P services. Then move funds into your non-custodial wallet, then use it for gambling. If you win big, exchange funds from instant exchange to make it fresh and cut the connection from the gambling sites. So you will not face any issues later.