What banks can work with crypto exchanges?

After moving from Australia to Georgia (the country), I found it impossible to use local banks to deposit fiat to crypto exchanges such as Binance and Kraken. I can use local banks to deposit into local crypto exchanges in small amounts, but they have terrible spreads and the threshold is too low to be useful.

People in Eastern Europe, how do you deposit fiat (say up to $500k USD) to crypto exchanges and withdraw from them? What banks do you use? Do people just go to Switzerland and bank there? The entire system is so difficult that it becomes unworkable.

Of course some will say buy IBIT or ETHA using IBKR or whatever, but these are ETFs and not real cryptos. Not your keys, not your coins.