Many posts in other forums have reported their mowers having this problem return or unresolved even after complete overhauls which included from cleaning/lubricating/adjusting/replacing axles, pulleys and bearings, checking the pinion gear and ratchet key, to overhauling/replacing the transmission.
When I replaced a Honda OE drive belt with an aftermarket belt, the mower immediately stopped reversing no matter how it was adjusted. Changing to a new Honda OE belt immediately resolved the problem. A simple way to check if the belt is the problem is with the transmission cable properly adjusted and disengaged, turn the mower over and turn a rear wheel by hand and observe if the transmission pulley slides under the belt. If it doesn't, the belt is grabbing and isn't allowing the Smart Drive slip clutch transmission to reverse. Would like to hear if this resolves some non-reversing problems.