So, eliminating the exchange blocking you, it's something you did, how far would would you go down the KYC path to get access back to an exchange account for how much money?. And would it matter about the exchange. Taking CoinEx they have been around for years and have a fairly good reputation, I would be more willing to give them some info about me then some other ones.
I would be careful with CoinEx, they look ok for now and I think they are connected with one mining pool, but like any other centralized exchange they can easily freeze your account.
If I want to exchange larger amount of money I would first look for direct p2p trading, and if that wouldn't work than I would be ready to pass kyc if asked by exchange.
Back in the early 2019 I sent pretty decent amount of stablecoin to Binance in order to stock up on bitcoin, and while waiting for the right time to buy, my mobile phone died leaving me without the access to Google authenticator.
I don't know what you are doing now with your 2fa codes, but I would suggest switching to Aegis app (instead of Google authenticator) and doing backup on different device like your computer.
You can even use KeePass as reserve option for storing backup codes in case something happens with your phone again.
That was the only exchange I ever did KYC, and will probably stay like that since I totally gave up on trading and I found better (and cheaper) ways to buy/sell bitcoin (mostly its directly from someone IRL).
This is much better option and I prefer it myself, but there are different risks involved with this method.