According to my experience, there is nothing faster than SEPA. I also use wire transfer option on cex (
https://cex.io/) because it doesnt charge any fees. 3 days to transfer fiat to exchange is rather quickly. Usually, the intervention of the third parties slows down the transaction process. On cex it takes from 3 to 5 days to transact fiat.
Yes. I guess this is where the stablecoin lacks.
I mean normally between two exchanges the fastest way to exchange money is using either crypto currency (which you do not want) or using stablecoins like USDT in order to make the transaction faster. If the two exchanges you would like to exchange the currency doesn't give you the option to deposit or withdraw USDT or anything similar to that (USDC for example) than it is lacking both on USDT part and for exchange as well.
USDT should be capable of helping you with stuff like that because that's the whole point of that token whereas the exchange should allow you to do that in order to get more trading from that type of currency and more trading would equal to more profits (they would probably profit from the withdrawal as well).