Our last night in London we're staying upstairs in the Paddington Hilton.
I've heard that some airlines allow one to check their baggage for outgoing flights at the Paddington HEX station. Is American Airlines one of them? Whats the drill?

yes, American Airlines passengers can check-in at Paddington. The desk is open from 5am to 9pm. It's very straightforward - you'll see the check-in desks before you get to the Heathrow Express train. Just check in there instead of at the airport and hop on the next train!

The check-in at Paddington is long gone. Unfortunately you will need to check bags at the airport.

AAFF is right. No, you cannot check in at Paddington for American Airlines. According to Heathrow Express' website,
http://www.heathrowexpress.com/
you can check-in at Paddington for the following airlines:
Air Canada
Austrian Airlines
Singapore Airlines
bmi
Varig Brazilian
LOT
Lufthansa
Thai Airways
SAS

It was a sad day when BritAir, in their budget-cutting wisdom, discontinued the very convenient Paddington check in. That was our main reason for paying the extra and taking H'row Express. Now we schlep our bags onto the Piccadilly line and save $$ instead. But I still miss that convenience, which meant we could walk past the long checkin lines at Heathrow.

On a side note, when we flew back last November we used the self-checkin kiosk in Terminal 4. It worked just fine, and was quick and painless. Now I'm wondering, why don't they install one at Paddington? Hmm, maybe I'll suggest that. Not that they are terrifically responsive to my suggestions...