I've recently started an experiment to send data deletion requests to 600 data brokers and document what happens. It's dark patterns all the way down.
The solution is to escalate your request to the local data protection agency (attorney general in case of California). I believe that if enough of us do this it will make a difference, even in the case of Amazon.
Following this realization we've recently added an optional features which will follow up with you some time after a request is made, and depending on the outcome, offer to automate the escalation process.