It looks like you've got what you wanted, but I think in 12 weeks or so you'll probably find out he's signed a pre-contract agreement with a Juventus, AC Milan etc and he'll leave on a free.
I don't think Barcelona would go for Sanchez, for the same reason I don't think they'll go for Aguero but as you say there aren't many obvious solutions. They might opt for a short term fix in which case Sanchez might work. £100m is OK for a young player, but not for a player who will give you one season.
It looks like hes staying but signing a pre contract with a foreign club in january makes no sense, if he waits till the summer he ll get a better deal. He ll have the option of the english clubs, including city, if youre still interested.
Barca selling Neymar might start some unexpected chain of events though.