I would bet on a mis-adjusted drive cable. There should typically be 0.5-1' of 'play' in the drive bail before it begins to engage. On your Honda, does the drive cable pull on a movable tensioner pulley, and that tensions the belt to drive the mower?There is no tensioner pully, but a tensioner arm that moves something around the transmission area and lets me get the drive belt out. I'm going to try to get it apart today.

1. Honda Harmony Lawn Mower Manual

Honda Harmony Lawn Mower Manual

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I'll post pictures. You are right that the cable does require some free play. It feels right to me though.