Some DPs:
I hadn't heard back from AMEX after ~10 days, so phoned them and asked for an update. Unfortunately, this wasn't sufficient for AMEX. I asked what constituted a "utility bill", but they couldn't give me examples - just that it was one of the categories of accepted ID. I'll have to wait until the US HSBC account is opened.
Interestingly, they only want to confirm my full name, not my residential address.
I called HSBC USA today after hearing nothing back from them (application made ~9 days ago). The woman on the phone was confused by the status of my account, as it was "Pending" but didn't specify why. After putting me on hold and calling the account opening team to check, she confirmed that it was pending because I had opened by AU HSBC account less than 30 days ago. Apparently once that period is over and I call back, they will open the account.
Hopefully I'll have a BofA account open in a fortnight or so; so will wait for a statement to generate and then go back to AMEX. Out of interest, does anybody know how long they will keep an application in a pending state while they wait for documents to be provided?