Would using an intermediary wallet to receive gambling funds be the solution?
A temporary solution it will be actually but not one which you can always count on. In other to avoid restrictions and not allowing your account getting some reputation that will affect your funds and this is why exchanges should be used for the purpose of changing and trading of crypto assets, other third party services shouldn't be carried out often on exchanges, particularly the ones they mentioned in their terms, for funding of your gambling wallets, you can always do that from a non custodial wallet too and save your self the hitch that comes with the exchanges. These wallet sometimes charges even cheaper fees as compared to the fees exchanges do charge, so they are a better option.
At least the OP received a warning and not freezing his funds right away. Much better to use your own wallet first like electrum (which you don't need a lot of storage) or other third party wallets that you can only use as a intermediary wallet. So you won't directly connect your exchange from the gambling site. I believe, that's one solution. These exchanges may not want to be associated with any other gambling site even if the OP mentioned that the gambling site is legit and license. Still, it is a gambling site.