The gearbox is remotely mounted from the engine (at least it is in the very early (Moss box) +8. I'm assuming the same for the +4, so it may be quicker / easier just to lift the engine?

Graham (G4FUJ)

Sold L44FOR 4/4 Giallo Fly
'09 Gen2 MINI Cooper ragtop
'90 LR 90 SW