Neither their website nor their BestChange listing said a single word about KYC being required for my exchange pair.
Are you sure? You didn't read this? It's on their website -
https://www.go-go.exchange/en/rules/aml-kyc-policy/By making an exchange through their platform it means you accepted their terms of service and policies and honestly freezing one's money is very unfair but legally, you can't win the case. You either accept the annoying KYC verification or say bye bye to the money.
Next time when looking for a no KYC exchange, Bestchange is the last place you should look at. Try the above that have been suggested or kycnot.me