I've had two situations with AMEX where they came back later and cleared up promotional miscalculations. Granted each took several months, but I didn't prompt them they just did it.
One related to a holiday APR which was apparently supposed to extend until the purchases were paid off, so they credited back some interest cost.
The other was for a BT offer on a new EDP that wasn't available after sign up. They created a window for BT to be done a few months ago.
Eventually I would expect you will see any interest credited off.
OP- also you can look at your first statment...on around page 4 it will have the promotional 0% with the end date. You can send them that too. Also make sure they have a record for all of your payments being on time.
Good luck in getting this squared away.
Heard back. 0% was turned on until next November and interest was refunded. 
Congrats, thanks for the update.
@Anonymous wrote:Signed up for the Blue Cash Preferred -- $150 bonus + 5% on $4,000 in travel expenses back in August. It came with a 0% intro APR.
Amex is now trying to charge me interest.
Went on chat, he told me 0% purchase APR wasn't included... I told him I had a screenshot of my offer and he opened an investigation... I guess I'll find out at some point? The agent just said "save your screenshot, they'll notate the result on your account." I don't really know what that means, and will probably call by week's end just to follow up.
Just wanted to remind you to save your offer screenshots. Funnily enough, I thought 12 months of 0% intro APR was standard on the BCP?
Wow this is so crazy same thing happened to me... nobody fixed it i had the PRG , Blue Cash Preferred and Everyday Preferred.. Closed all just because no one resloved my issue. Hope its different for you.