Can I transfer the BTC from my current address, to an address that no government can ever link to me?
Yes that is why mixers existed or you can manually convert your Bitcoins to an Altcoin like monero and then convert it back to Bitcoin. Though needs a lot of work but will possibly work on what you intended to do with your Bitcoins.
Centralized exchanges really has taxes on every transactions we made it is because they are compliant to regulations imposed by central banks.