Hi Eugene,
I’d get the advice of a gearbox specialist. I can see that replacing gearbox rather than repairing it makes sense but it might depend on the mileage of the current gearbox compared to the donor gearbox. I’d also say £10k is not a big budget so you will have to be very careful when it comes to buying a vehicle. I would advise either buying something old with low mileage that has been well cared for or maybe looking at self builds with service history.
Good luck!
Gary