Thanks all.

First flight is LHR - ORD.

At ORD I will need to get from T5 to T3 for the AA flight. If the bags were tagged for the onward flight (as I would normally do) then I could re-check straight after customs.

I think I'll go with LoM's suggestion and re-check with AA - I guess this means lugging my bag to T3 and finding the AA desk. Advantage is I'll have a better idea if the last connection is viable by then. US weather is making this whole adventure look more and more shakey!