I used Chase CDW and it took 21 days from the time I sent the first document in until a check came in the mail.

The primary benefit of using AMEX premium car rental is that it becomes primary insurance, but since you’ll be in a foreign country your basic Amex car rental protection will be primary so I think you’re wasting your money paying for the premium one.

Just note, in my experience, if you damage the car and intend to rely on CC insurance you will be paying for damages on the spot and then have to wait to get reimbursed. Rental car companies, especially in foreign countries, are not going to deal with Chase or Amex to get a claim taken care of.