To clarify about neutral drain (as you may know) ... the transmission must operate in agitate mode (~1 minute should normally be enough, longer may be needed when the parts get worn or in cold ambient temperatures if the transmission oil is thickened) before a drain period occurs to preset the neutral drain components. It won't neutral drain if the timer is set directly to the drain period after a cycle (or spin) has ended (without agitation occurring first).
There's really no need to change the motor coupler unless it's broken, cracked, loose on the motor or transmission shaft, or otherwise obviously deteriorated in some way. However, you may want to change it anyway if the machine still has the old-style coupler that's all plastic (without metal inserts). The newer style fits tighter, requires more "pounding" to get properly seated (must be flush with the ends of the shafts). Be sure to pound directly on the metal insert, not on the plastic part (I use a hex socket of appropriate size).