It also says: This offer is also not available to applicants who have or have had this product., and that provision will be enforced.
Yes, always apply without signing in. I assume you have never had the Premier Rewards Gold card?
You cannot "convert" a charge card to a credit card. You will need to submit a new application for the Everyday Preferred before cancelling the Premier Rewards Gold.
I was approved for the credit card last night but have had it before. I called AMEX and asked if I will get the bonus. I was told that because I had the card prior to May 2014 when they changed the rule, I am eligible for the bonus.