Use
22G1040 and change layshaft and end shims.
Original is stamped
DAM3168 and the 29 tooth gear is smaller in diameter 3" than the std ratio
22G927 which is 1/8" wider. One of the Mini gearboxes most sought after is the late 4 synchro remote box that has close ratio gears. The most certain identification is done be inspecting the laygear. If it is a 22G1040/DAM3168 laygear you have a close ratio box. While you are inspecting the laygear be sure to check the inner surface of the laygear which serves as the outer race of the layshaft bearings. This surface can breakdown resulting in premature failure of both the bearing and the shaft.
Ist motion shaft to go with this has 18teeth--22G1371 or
DAM3167