My mixer looks simular to yours with the exception mine has a U shaped "yoke" around the drum that makes the pivot point be almost 1/2 way between the gear bottom and the mouth of the drum. In fact as I am typing I am realizing that if you let the release on my dump and let go of the wheel the drum goes to a vertical position and no cement spills out unlike yours where it flops all the cement on the ground..
As for yours, The best way would be as someone else metioned to change the pivot so it is more toward the center of gravity.
Mine also uses a ships wheel style dump wheel. It is almost 4' in Diameter. This wheel allows very precice control of dump. It being a wheel you do not have that moment a heavy loaded lever reaches the top of its arc and you have to go from pull from one side to push from the other to restrain the load on the leaver. Also if you slip and it flops you have a spinning wheel rather than a swinging bat.