How certain are of you of the diagnosis?
I know you said the dealer wants £3k but has he seen or did you just ring up and ask “how much for a new gearbox?”
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Had an issue with the gears on my Transit back in Jan, it would give me first, or very reluctantly second, nothing else. I imediately thought new gearbox required and statrted looking on the interweb for one, properly expensive! Slept on it, had another look in the morning, started taking things apart, gear lever OK, cables look fine, selector unit on top of the gear box feels very, very stiif. Bearing inside there had seized. Full instructions on the Transit forum, took about 6hrs for a complete novice like me to remove strip and rebuild it, new bearing was £15.
Anyway, point is, are you certain the box is goosed, or is this merely an assumption? Check some less expensivde stuff first!