I talked to Amex customer service on the phone and the reps. there didn't seem too sure whether charges through officialpayments.com wouldn't be eligible. But they didn't see anything that would rule it out.

The stuff they exclude are things like cash advances and the annual fee of the card.

But just to make sure I logged in and got a written statement saying the charges would count and would also count towards the 10,000 MQM mileage boost.

Also got an email from Officialpayments.com saying they process multiple charges. Might have to do it over the phone rather than through the web site.

I also requested a credit increase from Amex but they said 7-10 days before an answer!