I would go for it then Laurence and change the sockets. You should be able to unplug the Existing High Level Brake Lamp and change that end on the bench.
That just leaves the car end. The 'Y' Splitter length will more than make up for the shortend cables and will never need to be removed once fitted.
To make fitting the new 'Car End' connector, you may be able to gain some length in that cable to temporarily pull forward from further under the spare wheel well??
It is worth having a look / feel past the cables next point where it is fixed to the body frame. There is usually some slack there to borrow

.
Happy hunting