Hi elizadoo,
I never got the option in MMB to to pay for an upgrade. This may be, as meeshi pointed, out because it's not a BA ticket. Equally, I've only ever been offered upgrades on point to point itineraries, which wasn't the case for this journey.
As I knew AA couldn't offer WTP I did ask in LHR T5 on my outbound leg who to ask for an airport upgrade - BA or AA. The CS agent suggested talking to the BA staff in LAX. As it happens, the flight from LAX was packed (1 seat left in WTP at T-48) so no upgrade was on offer.
FWIW, you could also try ringing BA about upgrading before your return journey starts. A BA agent did suggest that to me, as once the journey has started they would have more control over the ticket. They may only be able to re-price the ticket for you though, rather than giving you a POUG offer.
Finally, for future trips where you might use the A380 (MIA from Nov 2014?), I found the upper deck WT was quite good for an economy seat (I'm a mere mortal who only gets to travel Y). Better than the standard new WT in that it was very quiet (for a jet) and I managed to get more sleep than I ever have in Y. The side bins are very useful too!
Hope some of that is of use!
mrkflyer