We used coinbase for over a year with 2fa and it was perfectly fine.
This is in direct contradiction with your question! Every single transaction you have sent using Coinbase are already linked together and to your account and your identity. It would be trivial for anyone with legit beef to acquire the link too.
That goes with any other centralized services.
What you need is a custom made application where it uses some sort of mixing service for each payment. Either a centralized one through an API or participate in CoinJoin but both of these methods could have limitations such as not being able to pay anything below a certain amount (eg. <0.01
BTC) or having to only pay round numbers, etc.