3/4" is a lot of slop in the prop shaft and as Mr. Jestor recommended time for some service work......my first question however is what in the LU can fail and allow the prop shaft to move to and fro 3/4". However, if you will reassess your measurement, a slight back and forth movement of the prop/locked to the shaft, by your pushing forward on it and releasing is the action of the overrun clutch and is normal. If in doubt, go to a dealer and grasp the prop on a brand new engine and push it forward. Movement is normal if like what you experience.
Mark