Ice... i see you are confused now...
as i understand, the half cut is a M42 e36 manual, with long shaft,etc...
you can plonk in the whole engine, gearbox, longshaft, gear linkage.. no problem, no cutting..only works is the engine side, exhaust headers, mountings, air box and wirings...
what Fab is saying, you can use the gearbox that came with the halfcut, only the rear diff needs to be changed to match ratio of the box final drive which is 1:1..
the e36 diff wont be able to fit in, unless you swap the innards of the diff.. so look for a e34 medium housing which is a 3.45 or look for a e28 one which is a 3.25 or a 3.15..
it terms of how you do it, a good mechanic will be able to sort it out for you, BG did this swap for this owner here without much fuss, go have a chat with them..
happy modding