You say that the neighbour's cottage is in the way, but is there a way you could possibly run external Cat5e cable? - maybe along his gutter line so it is not seen?
The cottage is only in the way wrt where the router currently is.
I wouldn't be able to get a direct line of sight to the garage from there.
I could run cat 5 cable into the cellar and then onto the drive, but to make it neat would have to go cut into the drive. Not impossible though. It might be the cheaper option as well looking at the price of the wireless hardware