Bmw K1300GT broken gearbox

Lovely bike, everything is working apart from front seat heating... gearbox went, shifts up to fourth, finds neutral too, but wont rake 5th. The engine alone is worth 1500 quid, panniers 400, fairings close to a grand... heartbreaking, but fixing it is too expensive. Then theres exactly, electric screen, heated grips, wheels and so on. Worth well over 4 k in parts, I dont have the time. Donor, or for someone who wants to take on the challenge to fix it. The parts to do it should be less than 1000, but the labour makes it unfeasible.