I do thank those who responded with possible remedies to my issue. It is a shame no on from Honda so much as acknowledged any of my pleas for help I sent them. I filed that under "Honda Provides Great Customer Service" ... /sarc
As I have stated within this chain of messages, I have both attempted to resolve this issue myself numerous times and I have also taken it to an "authorized Honda service center" several times. Nothing resolved my issue.
UNTIL NOW ....
Yesterday I pulled both wheels of my mower, I cut two pieces of steel pipe I had on hand to a length equal to the width of the pinion gears, removed the ratchet keys, and replaced the pinion gear on each side with a piece of pipe.
My mower is no longer self-propelled, but for the first time in nearly two years I was able to mow my lawn without having to stop and reassemble all the components behind one or the other wheels. This will get me by until I do my research and purchase a new mower... and I can guarantee you that it will not be a Honda.