You WILL have to support the transmission BEFORE you separate the engine from it.
The engine, transmission and drive axle are bolted together as a unit but the drive axle housing is free to pivot because it is mounted in a trunnion yoke on the front end of the frame. If you don't support the trans, it is going to drop (pivot in frame) when the engine comes free.
As far as cushion mounts for the engine, those are basically to help minimize the chances of cracking the engine block due to stresses of frame flexing. Yes, the frame of a forklift actually flexes, no matter how stiff and rigid it looks or seems it ought to be.