Ask each service before depositing, if there is no answer try another service or avoid KYCed service.
I don't think proactively asking them can help, because as centralized exchanges, they have Terms of Service that stay on their sides. They can write some vague phrases in their terms on AML, that will be used in case they need to defend themselves than protect their customers.
You can ask, but in my opinion, it won't be helpful for you.
I agree with you about using no-KYC exchanges, it's safer.
Bitcoin Q&A: Blacklists, Taint, and Wallet FingerprintingWhy KYC is extremely dangerous – and uselessTo reduce the possibility of your coins being restricted as high risk send them to several addresses before depositing. for example:
Your coins --> New wallet address --> New wallet address --> New wallet address --> New wallet address --> exchange service you want to deposit to, with random fees.
Avoid combining inputs or send round number or all bitcoin in that wallet to another address. It's not good for privacy too.